random.po

# Copyright (C) 2001 Python Software Foundation
# This file is distributed under the same license as the Python package.
#
# Translators:
# Allen Wu <allen91.wu@gmail.com>, 2021
# Dr.XYZ <dr.xyz.tw@gmail.com>, 2025
msgid ""
msgstr ""
"Project-Id-Version: Python 3.14\n"
"Report-Msgid-Bugs-To: \n"
"POT-Creation-Date: 2025-12-20 00:15+0000\n"
"PO-Revision-Date: 2025-03-07 19:17+0800\n"
"Last-Translator: Dr.XYZ <dr.xyz.tw@gmail.com>\n"
"Language-Team: Chinese - TAIWAN (https://github.com/python/python-docs-zh-"
"tw)\n"
"Language: zh_TW\n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
"Content-Transfer-Encoding: 8bit\n"
"Plural-Forms: nplurals=1; plural=0;\n"
"X-Generator: Poedit 3.5\n"

#: ../../library/random.rst:2
msgid ":mod:`!random` --- Generate pseudo-random numbers"
msgstr ":mod:`!random` --- 產生偽隨機數"

#: ../../library/random.rst:7
msgid "**Source code:** :source:`Lib/random.py`"
msgstr "**原始碼：**\\ :source:`Lib/random.py`"

#: ../../library/random.rst:11
msgid ""
"This module implements pseudo-random number generators for various "
"distributions."
msgstr "本章中所提及的 module（模組）用來實現各種分佈的虛擬隨機數產生器。"

#: ../../library/random.rst:14
msgid ""
"For integers, there is uniform selection from a range. For sequences, there "
"is uniform selection of a random element, a function to generate a random "
"permutation of a list in-place, and a function for random sampling without "
"replacement."
msgstr ""
"對於整數，可以從範圍中進行均勻選擇。對於序列，有一個隨機元素的均勻選擇，一個"
"用來原地 (in-place) 產生隨機排列清單的函式，以及一個用來隨機取樣不重置的函"
"式。"

#: ../../library/random.rst:19
msgid ""
"On the real line, there are functions to compute uniform, normal (Gaussian), "
"lognormal, negative exponential, gamma, and beta distributions. For "
"generating distributions of angles, the von Mises distribution is available."
msgstr ""
"在實數線上，有一些函式用於處理均勻分佈、常態分佈（高斯分佈）、對數常態分佈、"
"負指數分佈、gamma 分佈和 Beta 分佈。對於產生角度分佈，可以使用馮·米塞斯分佈 "
"(von Mises distribution)。"

#: ../../library/random.rst:23
msgid ""
"Almost all module functions depend on the basic function :func:`.random`, "
"which generates a random float uniformly in the half-open range ``0.0 <= X < "
"1.0``. Python uses the Mersenne Twister as the core generator.  It produces "
"53-bit precision floats and has a period of 2\\*\\*19937-1.  The underlying "
"implementation in C is both fast and threadsafe.  The Mersenne Twister is "
"one of the most extensively tested random number generators in existence.  "
"However, being completely deterministic, it is not suitable for all "
"purposes, and is completely unsuitable for cryptographic purposes."
msgstr ""
"幾乎所有 module 函式都相依於基本函式 :func:`.random`，此函式在半開放範圍 "
"``0.0 <= X < 1.0`` 內均勻地產生一個隨機 float（浮點數）。Python 使用 "
"Mersenne Twister（梅森旋轉演算法）作為核心的產生器，它產生 53 位元精度 "
"float，其週期為 2\\*\\*19937-1，透過 C 語言進行底層的實作既快速又支援執行緒安"
"全 (threadsafe)。Mersenne Twister 是現存最廣泛被驗證的隨機數產生器之一，但是"
"基於完全確定性，它並不適合所有目的，並且完全不適合加密目的。"

#: ../../library/random.rst:32
msgid ""
"The functions supplied by this module are actually bound methods of a hidden "
"instance of the :class:`random.Random` class.  You can instantiate your own "
"instances of :class:`Random` to get generators that don't share state."
msgstr ""
"該 module 提供的函式實際上是 :class:`random.Random` class（類別）中一個隱藏實"
"例的綁定方法 (bound method)。你可以實例化自己的 :class:`Random` 實例，以得到"
"不共享狀態的產生器。"

#: ../../library/random.rst:36
msgid ""
"Class :class:`Random` can also be subclassed if you want to use a different "
"basic generator of your own devising: see the documentation on that class "
"for more details."
msgstr ""
"如果你想使用你自己設計的基本產生器，:class:`Random` 也可以進行子類別化 "
"(subclass)。有關詳細資訊，請參考該類別的文件。"

#: ../../library/random.rst:40
msgid ""
"The :mod:`random` module also provides the :class:`SystemRandom` class which "
"uses the system function :func:`os.urandom` to generate random numbers from "
"sources provided by the operating system."
msgstr ""
":mod:`random` module 也提供了 :class:`SystemRandom` class，使用系統函式 :"
"func:`os.urandom` 從作業系統提供的來源產生隨機數。"

#: ../../library/random.rst:46
msgid ""
"The pseudo-random generators of this module should not be used for security "
"purposes.  For security or cryptographic uses, see the :mod:`secrets` module."
msgstr ""
"本章所提及的虛擬隨機數產生器不應該使用於安全目的。有關安全性或加密用途，請參"
"考 :mod:`secrets` module。"

#: ../../library/random.rst:52
msgid ""
"M. Matsumoto and T. Nishimura, \"Mersenne Twister: A 623-dimensionally "
"equidistributed uniform pseudorandom number generator\", ACM Transactions on "
"Modeling and Computer Simulation Vol. 8, No. 1, January pp.3--30 1998."
msgstr ""
"M. Matsumoto and T. Nishimura, \"Mersenne Twister: A 623-dimensionally "
"equidistributed uniform pseudorandom number generator\", ACM Transactions on "
"Modeling and Computer Simulation Vol. 8, No. 1, January pp.3--30 1998."

#: ../../library/random.rst:57
msgid ""
"`Complementary-Multiply-with-Carry recipe <https://code.activestate.com/"
"recipes/576707-long-period-random-number-generator/>`_ for a compatible "
"alternative random number generator with a long period and comparatively "
"simple update operations."
msgstr ""
"`進位互補乘法 (Complementary-Multiply-with-Carry) 用法 <https://code."
"activestate.com/recipes/576707-long-period-random-number-generator/>`_，可作"
"為隨機數產生器的一個可相容替代方案，具有較長的週期和相對簡單的更新操作。"

#: ../../library/random.rst:63
msgid ""
"The global random number generator and instances of :class:`Random` are "
"thread-safe. However, in the free-threaded build, concurrent calls to the "
"global generator or to the same instance of :class:`Random` may encounter "
"contention and poor performance. Consider using separate instances of :class:"
"`Random` per thread instead."
msgstr ""
"全域隨機數產生器和 :class:`Random` 的實例是執行緒安全的。然而，在自由執行緒構"
"建中，對全域產生器或同一 :class:`Random` 實例的並行呼叫可能會遇到爭用和性能不"
"佳。請考慮改為每個執行緒使用單獨的 :class:`Random` 實例。"

#: ../../library/random.rst:70
msgid "Bookkeeping functions"
msgstr "簿記函式 (bookkeeping functions)"

#: ../../library/random.rst:74
msgid "Initialize the random number generator."
msgstr "初始化隨機數產生器。"

#: ../../library/random.rst:76
msgid ""
"If *a* is omitted or ``None``, the current system time is used.  If "
"randomness sources are provided by the operating system, they are used "
"instead of the system time (see the :func:`os.urandom` function for details "
"on availability)."
msgstr ""
"如果 *a* 被省略或為 ``None``，則使用目前系統時間。如果隨機來源由作業系統提"
"供，則使用它們而不是系統時間（有關可用性的詳細資訊，請參考 :func:`os."
"urandom` 函式）。"

#: ../../library/random.rst:81
msgid "If *a* is an int, its absolute value is used directly."
msgstr "如果 *a* 為 int（整數），則直接使用其絕對值。"

#: ../../library/random.rst:83
msgid ""
"With version 2 (the default), a :class:`str`, :class:`bytes`, or :class:"
"`bytearray` object gets converted to an :class:`int` and all of its bits are "
"used."
msgstr ""
"如使用版本 2（預設值），:class:`str`、:class:`bytes` 或 :class:`bytearray` 物"
"件將轉換為 :class:`int`，並使用其所有位元。"

#: ../../library/random.rst:86
msgid ""
"With version 1 (provided for reproducing random sequences from older "
"versions of Python), the algorithm for :class:`str` and :class:`bytes` "
"generates a narrower range of seeds."
msgstr ""
"若使用版本 1（為復現於舊版本 Python 中產生隨機序列而提供），:class:`str` 和 :"
"class:`bytes` 的演算法會產生範圍更窄的種子 (seed)。"

#: ../../library/random.rst:90
msgid ""
"Moved to the version 2 scheme which uses all of the bits in a string seed."
msgstr "移至版本 2 方案，該方案使用字串種子中的所有位元。"

#: ../../library/random.rst:93
msgid ""
"The *seed* must be one of the following types: ``None``, :class:`int`, :"
"class:`float`, :class:`str`, :class:`bytes`, or :class:`bytearray`."
msgstr ""
"*seed* 必須是以下型別之一：``None``、:class:`int`、:class:`float`、:class:"
"`str`、:class:`bytes`、:class:`bytearray`。"

#: ../../library/random.rst:100
msgid ""
"Return an object capturing the current internal state of the generator.  "
"This object can be passed to :func:`setstate` to restore the state."
msgstr ""
"回傳一個物件，捕獲產生器的目前內部狀態。此物件可以傳遞給 :func:`setstate` 以"
"恢復狀態。"

#: ../../library/random.rst:106
msgid ""
"*state* should have been obtained from a previous call to :func:`getstate`, "
"and :func:`setstate` restores the internal state of the generator to what it "
"was at the time :func:`getstate` was called."
msgstr ""
"*state* 應該要從之前對 :func:`getstate` 的呼叫中獲得，並且以 :func:"
"`setstate` 將產生器的內部狀態恢復到呼叫 :func:`getstate` 時的狀態。"

#: ../../library/random.rst:112
msgid "Functions for bytes"
msgstr "回傳位元組的函式"

#: ../../library/random.rst:116
msgid "Generate *n* random bytes."
msgstr "產生 *n* 個隨機位元組。"

#: ../../library/random.rst:118
msgid ""
"This method should not be used for generating security tokens. Use :func:"
"`secrets.token_bytes` instead."
msgstr ""
"此方法不應使用於產生安全性權杖 (Token)。請改用 :func:`secrets.token_bytes`。"

#: ../../library/random.rst:125
msgid "Functions for integers"
msgstr "回傳整數的函式"

#: ../../library/random.rst:130
msgid "Return a randomly selected element from ``range(start, stop, step)``."
msgstr "傳回從 ``range(start, stop, step)`` 中隨機選擇的元素。"

#: ../../library/random.rst:132
msgid ""
"This is roughly equivalent to ``choice(range(start, stop, step))`` but "
"supports arbitrarily large ranges and is optimized for common cases."
msgstr ""
"這大致相當於 ``choice(range(start, stop, step))``，但支援任意大的範圍，並針對"
"常見情況進行了最佳化。"

#: ../../library/random.rst:135
msgid "The positional argument pattern matches the :func:`range` function."
msgstr "位置引數模式與 :func:`range` 函式相符。"

#: ../../library/random.rst:137
msgid ""
"Keyword arguments should not be used because they can be interpreted in "
"unexpected ways. For example ``randrange(start=100)`` is interpreted as "
"``randrange(0, 100, 1)``."
msgstr ""
"不應使用關鍵字引數，因為它們可能會以意想不到的方式被直譯。例如 "
"``randrange(start=100)`` 會被直譯為 ``randrange(0, 100, 1)``。"

#: ../../library/random.rst:141
msgid ""
":meth:`randrange` is more sophisticated about producing equally distributed "
"values.  Formerly it used a style like ``int(random()*n)`` which could "
"produce slightly uneven distributions."
msgstr ""
":meth:`randrange` 在產生均勻分佈的值方面更為複雜。以前，它使用像 "
"``int(random()*n)`` 這樣的樣式，這可能會產生稍微不均勻的分佈。"

#: ../../library/random.rst:146
msgid ""
"Automatic conversion of non-integer types is no longer supported. Calls such "
"as ``randrange(10.0)`` and ``randrange(Fraction(10, 1))`` now raise a :exc:"
"`TypeError`."
msgstr ""
"已經不再支援非整數類型到等效整數的自動轉換。像是 ``randrange(10.0)`` 和 "
"``randrange(Fraction(10, 1))`` 的呼叫將會引發 :exc:`TypeError`。"

#: ../../library/random.rst:153
msgid ""
"Return a random integer *N* such that ``a <= N <= b``.  Alias for "
"``randrange(a, b+1)``."
msgstr ""
"回傳一個隨機整數 *N*，使得 ``a <= N <= b``。為 ``randrange(a, b+1)`` 的別名。"

#: ../../library/random.rst:158
msgid ""
"Returns a non-negative Python integer with *k* random bits. This method is "
"supplied with the Mersenne Twister generator and some other generators may "
"also provide it as an optional part of the API. When available, :meth:"
"`getrandbits` enables :meth:`randrange` to handle arbitrarily large ranges."
msgstr ""
"回傳一個具有 *k* 個隨機位元的非負 Python 整數。此方法會隨 Mersenne Twister 產"
"生器一起提供，一些其他的產生器也可能將其作為 API 的可選部分。如果可用，:meth:"
"`getrandbits` 使 :meth:`randrange` 能夠處理任意大的範圍。"

#: ../../library/random.rst:164
msgid "This method now accepts zero for *k*."
msgstr "此方法現在接受 *k* 為零。"

#: ../../library/random.rst:169
msgid "Functions for sequences"
msgstr "回傳序列的函式"

#: ../../library/random.rst:173
msgid ""
"Return a random element from the non-empty sequence *seq*. If *seq* is "
"empty, raises :exc:`IndexError`."
msgstr ""
"從非空序列 *seq* 回傳一個隨機元素。如果 *seq* 為空，則引發 :exc:"
"`IndexError`。"

#: ../../library/random.rst:178
msgid ""
"Return a *k* sized list of elements chosen from the *population* with "
"replacement. If the *population* is empty, raises :exc:`IndexError`."
msgstr ""
"回傳從 *population* 中重置取樣出的一個大小為 *k* 的元素 list。如果 "
"*population* 為空，則引發 :exc:`IndexError`。"

#: ../../library/random.rst:181
msgid ""
"If a *weights* sequence is specified, selections are made according to the "
"relative weights.  Alternatively, if a *cum_weights* sequence is given, the "
"selections are made according to the cumulative weights (perhaps computed "
"using :func:`itertools.accumulate`).  For example, the relative weights "
"``[10, 5, 30, 5]`` are equivalent to the cumulative weights ``[10, 15, 45, "
"50]``.  Internally, the relative weights are converted to cumulative weights "
"before making selections, so supplying the cumulative weights saves work."
msgstr ""
"如果指定了 *weights* 序列，則根據相對權重進行選擇。另外，如果給定 "
"*cum_weights* 序列，則根據累積權重進行選擇（可能使用 :func:`itertools."
"accumulate` 計算）。例如，相對權重 ``[10, 5, 30, 5]`` 等同於累積權重 ``[10, "
"15, 45, 50]``。在內部，相對權重在進行選擇之前會轉換為累積權重，因此提供累積權"
"重可以節省工作。"

#: ../../library/random.rst:190
msgid ""
"If neither *weights* nor *cum_weights* are specified, selections are made "
"with equal probability.  If a weights sequence is supplied, it must be the "
"same length as the *population* sequence.  It is a :exc:`TypeError` to "
"specify both *weights* and *cum_weights*."
msgstr ""
"如果既未指定 *weights* 也未指定 *cum_weights*，則以相等的機率進行選擇。如果提"
"供了加權序列，則該序列的長度必須與 *population* 序列的長度相同。它是一個 :"
"exc:`TypeError` 來指定 *weights* 和 *cum_weights*。"

#: ../../library/random.rst:195
msgid ""
"The *weights* or *cum_weights* can use any numeric type that interoperates "
"with the :class:`float` values returned by :func:`random` (that includes "
"integers, floats, and fractions but excludes decimals).  Weights are assumed "
"to be non-negative and finite.  A :exc:`ValueError` is raised if all weights "
"are zero."
msgstr ""
"*weights* 或 *cum_weights* 可以使用任何與 :func:`random` 所回傳的 :class:"
"`float` 值（包括整數、float 和分數，但不包括小數）交互操作 (interoperates) 的"
"數值類型。權重假定為非負數和有限的。如果所有權重均為零，則引發 :exc:"
"`ValueError`。"

#: ../../library/random.rst:201
msgid ""
"For a given seed, the :func:`choices` function with equal weighting "
"typically produces a different sequence than repeated calls to :func:"
"`choice`.  The algorithm used by :func:`choices` uses floating-point "
"arithmetic for internal consistency and speed.  The algorithm used by :func:"
"`choice` defaults to integer arithmetic with repeated selections to avoid "
"small biases from round-off error."
msgstr ""
"對於給定的種子，具有相等權重的 :func:`choices` 函式通常產生與重複呼叫 :func:"
"`choice` 不同的序列。:func:`choices` 使用的演算法使用浮點運算來實現內部一致性"
"和速度。:func:`choice` 使用的演算法預設為整數運算和重複選擇，以避免捨入誤差產"
"生的小偏差。"

#: ../../library/random.rst:210
msgid "Raises a :exc:`ValueError` if all weights are zero."
msgstr "如果所有權重均為零，則引發 :exc:`ValueError`。"

#: ../../library/random.rst:216
msgid "Shuffle the sequence *x* in place."
msgstr "將序列 *x* 原地 (in place) 隨機打亂位置。"

#: ../../library/random.rst:218
msgid ""
"To shuffle an immutable sequence and return a new shuffled list, use "
"``sample(x, k=len(x))`` instead."
msgstr ""
"要打亂一個不可變的序列並回傳一個新的被打亂的 list（串列），請使用 "
"``sample(x, k=len(x))``。"

#: ../../library/random.rst:221
msgid ""
"Note that even for small ``len(x)``, the total number of permutations of *x* "
"can quickly grow larger than the period of most random number generators. "
"This implies that most permutations of a long sequence can never be "
"generated.  For example, a sequence of length 2080 is the largest that can "
"fit within the period of the Mersenne Twister random number generator."
msgstr ""
"請注意，即使對於較小的 ``len(x)``，*x* 的置換總數也會快速成長到大於大多數隨機"
"數產生器的週期。這意味著長序列的大多數置換永遠無法產生。例如，長度為 2080 的"
"序列是 Mersenne Twister 隨機數產生器週期內可以容納的最大序列。"

#: ../../library/random.rst:227
msgid "Removed the optional parameter *random*."
msgstr "移除可選參數 *random*。"

#: ../../library/random.rst:233
msgid ""
"Return a *k* length list of unique elements chosen from the population "
"sequence.  Used for random sampling without replacement."
msgstr ""
"回傳從母體序列中選擇出的一個包含獨特元素、長度為 *k* 的 list。用於不重置的隨"
"機取樣。"

#: ../../library/random.rst:236
msgid ""
"Returns a new list containing elements from the population while leaving the "
"original population unchanged.  The resulting list is in selection order so "
"that all sub-slices will also be valid random samples.  This allows raffle "
"winners (the sample) to be partitioned into grand prize and second place "
"winners (the subslices)."
msgstr ""
"回傳包含母體元素的新清單，同時保持原始母體不變。產生的清單按選擇順序排列，因"
"此所有子切片也會是有效的隨機樣本。這允許抽獎獲獎者（樣本）分為大獎和第二名獲"
"獎者（子切片）。"

#: ../../library/random.rst:242
msgid ""
"Members of the population need not be :term:`hashable` or unique.  If the "
"population contains repeats, then each occurrence is a possible selection in "
"the sample."
msgstr ""
"母體成員不必是 :term:`hashable` 或唯一的。如果母體包含重複項，則每次出現都是"
"樣本中可能出現的一個選擇。"

#: ../../library/random.rst:245
msgid ""
"Repeated elements can be specified one at a time or with the optional "
"keyword-only *counts* parameter.  For example, ``sample(['red', 'blue'], "
"counts=[4, 2], k=5)`` is equivalent to ``sample(['red', 'red', 'red', 'red', "
"'blue', 'blue'], k=5)``."
msgstr ""
"可以一次指定一個重複元素，也可以使用可選的僅關鍵字 *counts* 參數指定重複元"
"素。例如 ``sample(['red', 'blue'], counts=[4, 2], k=5)`` 等同於 "
"``sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5)``。"

#: ../../library/random.rst:250
msgid ""
"To choose a sample from a range of integers, use a :func:`range` object as "
"an argument.  This is especially fast and space efficient for sampling from "
"a large population:  ``sample(range(10000000), k=60)``."
msgstr ""
"若要從整數範圍中選擇範例，請使用 :func:`range` 物件作為引數。這對於從大型母體"
"中取樣特別快速且節省空間：``sample(range(10000000), k=60)``。"

#: ../../library/random.rst:254
msgid ""
"If the sample size is larger than the population size, a :exc:`ValueError` "
"is raised."
msgstr "如果樣本大小大於母體大小，:exc:`ValueError` 會被引發。"

#: ../../library/random.rst:257
msgid "Added the *counts* parameter."
msgstr "新增 *counts* 參數。"

#: ../../library/random.rst:262
msgid ""
"The *population* must be a sequence.  Automatic conversion of sets to lists "
"is no longer supported."
msgstr "*population* 必須是一個序列。不再支援將 set 自動轉換為 list。"

#: ../../library/random.rst:266
msgid "Discrete distributions"
msgstr "離散分布"

#: ../../library/random.rst:268
msgid "The following function generates a discrete distribution."
msgstr "以下函式產生離散分佈。"

#: ../../library/random.rst:272
msgid ""
"`Binomial distribution <https://mathworld.wolfram.com/BinomialDistribution."
"html>`_. Return the number of successes for *n* independent trials with the "
"probability of success in each trial being *p*:"
msgstr ""
"`二項分佈 (Binomial distribution) <https://mathworld.wolfram.com/"
"BinomialDistribution.html>`_。回傳 *n* 個獨立試驗的成功次數，每個試驗的成功機"
"率為 *p*："

#: ../../library/random.rst:277
msgid "Mathematically equivalent to::"
msgstr "數學上等價於： ::"

#: ../../library/random.rst:279
msgid "sum(random() < p for i in range(n))"
msgstr "sum(random() < p for i in range(n))"

#: ../../library/random.rst:281
msgid ""
"The number of trials *n* should be a non-negative integer. The probability "
"of success *p* should be between ``0.0 <= p <= 1.0``. The result is an "
"integer in the range ``0 <= X <= n``."
msgstr ""
"試驗次數 *n* 應為非負整數。成功的機率 *p* 應在 ``0.0 <= p <= 1.0`` 之間。結果"
"是 ``0 <= X <= n`` 範圍內的整數。"

#: ../../library/random.rst:291
msgid "Real-valued distributions"
msgstr "實數分布"

#: ../../library/random.rst:293
msgid ""
"The following functions generate specific real-valued distributions. "
"Function parameters are named after the corresponding variables in the "
"distribution's equation, as used in common mathematical practice; most of "
"these equations can be found in any statistics text."
msgstr ""
"以下函式產生特定的實數分佈。函式參數以分佈方程中的對應變數命名，如常見的數學"
"實踐所示；這些方程式中的大多數都可以在任意統計文本中找到。"

#: ../../library/random.rst:301
msgid ""
"Return the next random floating-point number in the range ``0.0 <= X < 1.0``"
msgstr "回傳範圍 ``0.0 <= X < 1.0`` 中的下一個隨機浮點數"

#: ../../library/random.rst:306
msgid ""
"Return a random floating-point number *N* such that ``a <= N <= b`` for ``a "
"<= b`` and ``b <= N <= a`` for ``b < a``."
msgstr ""
"回傳一個隨機浮點數 *N*，當 ``a <= b`` 時確保 N 為 ``a <= N <= b`` 、``b < "
"a`` 時確保 N 為 ``b <= N <= a``。"

#: ../../library/random.rst:309
msgid ""
"The end-point value ``b`` may or may not be included in the range depending "
"on floating-point rounding in the expression ``a + (b-a) * random()``."
msgstr ""
"終點值 ``b`` 可能包含在範圍內，也可能不包含在範圍內，取決於運算式 ``a + (b-"
"a) * random()`` 中的浮點捨入。"

#: ../../library/random.rst:316
msgid ""
"Return a random floating-point number *N* such that ``low <= N <= high`` and "
"with the specified *mode* between those bounds.  The *low* and *high* bounds "
"default to zero and one.  The *mode* argument defaults to the midpoint "
"between the bounds, giving a symmetric distribution."
msgstr ""
"回傳一個隨機浮點數 *N*，使得 ``low <= N <= high``，並在這些邊界之間具有指定"
"的 *mode*。*low* 和 *high* 邊界預設為零和一。*mode* 引數預設為邊界之間的中"
"點，從而給出對稱分佈。"

#: ../../library/random.rst:324
msgid ""
"Beta distribution.  Conditions on the parameters are ``alpha > 0`` and "
"``beta > 0``. Returned values range between 0 and 1."
msgstr ""
"Beta（貝它）分布。參數的條件為 ``alpha > 0`` 和 ``beta > 0``。回傳值的範圍介"
"於 0 和 1 之間。"

#: ../../library/random.rst:330
msgid ""
"Exponential distribution.  *lambd* is 1.0 divided by the desired mean.  It "
"should be nonzero.  (The parameter would be called \"lambda\", but that is a "
"reserved word in Python.)  Returned values range from 0 to positive infinity "
"if *lambd* is positive, and from negative infinity to 0 if *lambd* is "
"negative."
msgstr ""
"指數分佈。*lambd* 為 1.0 除以所需的平均數。它應該不為零。（該參數將被稱為 "
"\"lambda\"，但這是 Python 中的保留字）如果 *lambd* 為正，則回傳值的範圍從 0 "
"到正無窮大；如果 *lambd* 為負，則回傳值的範圍從負無窮大到 0。"

#: ../../library/random.rst:336
msgid "Added the default value for ``lambd``."
msgstr "新增 ``lambd`` 的預設值。"

#: ../../library/random.rst:342
msgid ""
"Gamma distribution.  (*Not* the gamma function!)  The shape and scale "
"parameters, *alpha* and *beta*, must have positive values. (Calling "
"conventions vary and some sources define 'beta' as the inverse of the scale)."
msgstr ""
"Gamma（伽瑪）分佈。（*不是* Gamma 函式！）。形狀 (shape) 和比例 (scale) 參數 "
"*alpha* 和 *beta* 必須具有正值。（根據呼叫習慣不同，部分來源會將 'beta' 定義"
"為比例的倒數）。"

#: ../../library/random.rst:347
msgid "The probability distribution function is::"
msgstr "Probability distribution function（機率密度函式）是： ::"

#: ../../library/random.rst:349
msgid ""
"          x ** (alpha - 1) * math.exp(-x / beta)\n"
"pdf(x) =  --------------------------------------\n"
"            math.gamma(alpha) * beta ** alpha"
msgstr ""
"          x ** (alpha - 1) * math.exp(-x / beta)\n"
"pdf(x) =  --------------------------------------\n"
"            math.gamma(alpha) * beta ** alpha"

#: ../../library/random.rst:356
msgid ""
"Normal distribution, also called the Gaussian distribution. *mu* is the "
"mean, and *sigma* is the standard deviation.  This is slightly faster than "
"the :func:`normalvariate` function defined below."
msgstr ""
"常態分佈，也稱為高斯分佈。*mu* 是平均數，*sigma* 是標準差。這比下面定義的 :"
"func:`normalvariate` 函式快一點。"

#: ../../library/random.rst:361
msgid ""
"Multithreading note:  When two threads call this function simultaneously, it "
"is possible that they will receive the same return value.  This can be "
"avoided in three ways. 1) Have each thread use a different instance of the "
"random number generator. 2) Put locks around all calls. 3) Use the slower, "
"but thread-safe :func:`normalvariate` function instead."
msgstr ""
"多執行緒須注意：當兩個執行緒同時呼叫此函式時，它們可能會收到相同的傳回值。這"
"可以透過三種方式避免。1）讓每個執行緒使用隨機數產生器的不同實例。2）在所有呼"
"叫周圍加鎖。3）使用較慢但執行緒安全的 :func:`normalvariate` 函式代替。"

#: ../../library/random.rst:368 ../../library/random.rst:384
msgid "*mu* and *sigma* now have default arguments."
msgstr "*mu* 和 *sigma* 現在有預設引數。"

#: ../../library/random.rst:374
msgid ""
"Log normal distribution.  If you take the natural logarithm of this "
"distribution, you'll get a normal distribution with mean *mu* and standard "
"deviation *sigma*.  *mu* can have any value, and *sigma* must be greater "
"than zero."
msgstr ""
"對數常態分佈。如果你取此分佈的自然對數，你將獲得一個具有平均數 *mu* 和標準差 "
"*sigma* 的常態分佈。*mu* 可以為任何值，並且 *sigma* 必須大於零。"

#: ../../library/random.rst:382
msgid ""
"Normal distribution.  *mu* is the mean, and *sigma* is the standard "
"deviation."
msgstr "常態分佈。*mu* 是平均數，*sigma* 是標準差。"

#: ../../library/random.rst:390
msgid ""
"*mu* is the mean angle, expressed in radians between 0 and 2\\*\\ *pi*, and "
"*kappa* is the concentration parameter, which must be greater than or equal "
"to zero.  If *kappa* is equal to zero, this distribution reduces to a "
"uniform random angle over the range 0 to 2\\*\\ *pi*."
msgstr ""
"*mu* 是平均角度，以 0 到 2\\*\\ *pi* 之間的弧度表示，*kappa* 是濃度參數，必須"
"大於或等於零。如果 *kappa* 等於零，則此分佈在 0 到 2\\*\\ *pi* 的範圍內將減小"
"為均勻的隨機角度。"

#: ../../library/random.rst:398
msgid "Pareto distribution.  *alpha* is the shape parameter."
msgstr "Pareto distribution（柏拉圖分佈）。*alpha* 是形狀參數。"

#: ../../library/random.rst:403
msgid ""
"Weibull distribution.  *alpha* is the scale parameter and *beta* is the "
"shape parameter."
msgstr ""
"Weibull distribution（韋伯分佈）。*alpha* 是比例參數，*beta* 是形狀參數。"

#: ../../library/random.rst:408
msgid "Alternative Generator"
msgstr "替代產生器"

#: ../../library/random.rst:412
msgid ""
"Class that implements the default pseudo-random number generator used by "
"the :mod:`random` module."
msgstr "實現 :mod:`random` 模組使用的預設偽隨機數產生器的 class。"

#: ../../library/random.rst:415
msgid ""
"Formerly the *seed* could be any hashable object.  Now it is limited to: "
"``None``, :class:`int`, :class:`float`, :class:`str`, :class:`bytes`, or :"
"class:`bytearray`."
msgstr ""
"過去 *seed* 可以是任何可雜湊物件，但現在必須是以下類型之一：``None``、:class:"
"`int`、:class:`float`、:class:`str`、:class:`bytes`、:class:`bytearray`。"

#: ../../library/random.rst:420
msgid ""
"Subclasses of :class:`!Random` should override the following methods if they "
"wish to make use of a different basic generator:"
msgstr ""
"如果 :class:`!Random` 的子類別希望使用不同的基礎產生器，則應該覆寫以下方法："

#: ../../library/random.rst:425
msgid ""
"Override this method in subclasses to customise the :meth:`~random.seed` "
"behaviour of :class:`!Random` instances."
msgstr ""
"在子類別中覆寫此方法以自訂 :class:`!Random` 實例的 :meth:`~random.seed` 行"
"為。"

#: ../../library/random.rst:430
msgid ""
"Override this method in subclasses to customise the :meth:`~random.getstate` "
"behaviour of :class:`!Random` instances."
msgstr ""
"在子類別中覆寫此方法以自訂 :class:`!Random` 實例的 :meth:`~random.getstate` "
"行為。"

#: ../../library/random.rst:435
msgid ""
"Override this method in subclasses to customise the :meth:`~random.setstate` "
"behaviour of :class:`!Random` instances."
msgstr ""
"在子類別中覆寫此方法以自訂 :class:`!Random` 實例的 :meth:`~random.setstate` "
"行為。"

#: ../../library/random.rst:440
msgid ""
"Override this method in subclasses to customise the :meth:`~random.random` "
"behaviour of :class:`!Random` instances."
msgstr ""
"在子類別中覆寫此方法以自訂 :class:`!Random` 實例的 :meth:`~random.random` 行"
"為。"

#: ../../library/random.rst:443
msgid ""
"Optionally, a custom generator subclass can also supply the following method:"
msgstr "或者，自訂產生器子類別還可以提供以下方法："

#: ../../library/random.rst:447
msgid ""
"Override this method in subclasses to customise the :meth:`~random."
"getrandbits` behaviour of :class:`!Random` instances."
msgstr ""
"在子類別中覆寫此方法以自訂 :class:`!Random` 實例的 :meth:`~random."
"getrandbits` 行為。"

#: ../../library/random.rst:452
msgid ""
"Override this method in subclasses to customise the :meth:`~random."
"randbytes` behaviour of :class:`!Random` instances."
msgstr ""
"在子類別中覆寫此方法以自訂 :class:`!Random` 實例的 :meth:`~random.randbytes` "
"行為。"

#: ../../library/random.rst:458
msgid ""
"Class that uses the :func:`os.urandom` function for generating random "
"numbers from sources provided by the operating system. Not available on all "
"systems. Does not rely on software state, and sequences are not "
"reproducible. Accordingly, the :meth:`seed` method has no effect and is "
"ignored. The :meth:`getstate` and :meth:`setstate` methods raise :exc:"
"`NotImplementedError` if called."
msgstr ""
"使用 :func:`os.urandom` 函式從作業系統提供的來源產生隨機數的 Class。並非在所"
"有系統上都可用。不依賴於軟體狀態，並且序列不可復現。因此 :meth:`seed` 方法沒"
"有效果且被忽略。如果呼叫 :meth:`getstate` 和 :meth:`setstate` 方法會引發 :"
"exc:`NotImplementedError`。"

#: ../../library/random.rst:467
msgid "Notes on Reproducibility"
msgstr "關於 Reproducibility（復現性）的注意事項"

#: ../../library/random.rst:469
msgid ""
"Sometimes it is useful to be able to reproduce the sequences given by a "
"pseudo-random number generator.  By reusing a seed value, the same sequence "
"should be reproducible from run to run as long as multiple threads are not "
"running."
msgstr ""
"有時，能夠重現偽隨機數產生器給出的序列很有用。只要多執行緒未運行，透過重複使"
"用種子值，同一序列就應該可以被復現。"

#: ../../library/random.rst:473
msgid ""
"Most of the random module's algorithms and seeding functions are subject to "
"change across Python versions, but two aspects are guaranteed not to change:"
msgstr ""
"大多數隨機 module 的演算法和 seed 設定函式在 Python 版本中可能會發生變化，但"
"可以保證兩個方面不會改變："

#: ../../library/random.rst:476
msgid ""
"If a new seeding method is added, then a backward compatible seeder will be "
"offered."
msgstr "如果增加了新的 seed 設定函式，則將提供向後相容的播種器 (seeder)。"

#: ../../library/random.rst:479
msgid ""
"The generator's :meth:`~Random.random` method will continue to produce the "
"same sequence when the compatible seeder is given the same seed."
msgstr ""
"當相容的播種器被賦予相同的種子時，產生器的 :meth:`~Random.random` 方法將持續"
"產生相同的序列。"

#: ../../library/random.rst:485
msgid "Examples"
msgstr "範例"

#: ../../library/random.rst:487
msgid "Basic examples::"
msgstr "基礎範例： ::"

#: ../../library/random.rst:489
msgid ""
">>> random()                          # Random float:  0.0 <= x < 1.0\n"
"0.37444887175646646\n"
"\n"
">>> uniform(2.5, 10.0)                # Random float:  2.5 <= x <= 10.0\n"
"3.1800146073117523\n"
"\n"
">>> expovariate(1 / 5)                # Interval between arrivals averaging "
"5 seconds\n"
"5.148957571865031\n"
"\n"
">>> randrange(10)                     # Integer from 0 to 9 inclusive\n"
"7\n"
"\n"
">>> randrange(0, 101, 2)              # Even integer from 0 to 100 "
"inclusive\n"
"26\n"
"\n"
">>> choice(['win', 'lose', 'draw'])   # Single random element from a "
"sequence\n"
"'draw'\n"
"\n"
">>> deck = 'ace two three four'.split()\n"
">>> shuffle(deck)                     # Shuffle a list\n"
">>> deck\n"
"['four', 'two', 'ace', 'three']\n"
"\n"
">>> sample([10, 20, 30, 40, 50], k=4) # Four samples without replacement\n"
"[40, 10, 50, 30]"
msgstr ""
">>> random()                          # 隨機浮點數：0.0 <= x < 1.0\n"
"0.37444887175646646\n"
"\n"
">>> uniform(2.5, 10.0)                # 隨機浮點數：2.5 <= x <= 10.0\n"
"3.1800146073117523\n"
"\n"
">>> expovariate(1 / 5)                # 到達間隔平均為 5 秒\n"
"5.148957571865031\n"
"\n"
">>> randrange(10)                     # 0 到 9（含）的整數\n"
"7\\n\n"
"\n"
">>> randrange(0, 101, 2)              # 0 到 100（含）的偶數整數\n"
"26\\n\n"
"\n"
">>> choice(['win', 'lose', 'draw'])   # 從序列中隨機選取單一元素\n"
"'draw'\n"
"\n"
">>> deck = 'ace two three four'.split()\n"
">>> shuffle(deck)                     # 打亂串列\n"
">>> deck\n"
"['four', 'two', 'ace', 'three']\n"
"\n"
">>> sample([10, 20, 30, 40, 50], k=4) # 四個無重置的樣本\n"
"[40, 10, 50, 30]"

#: ../../library/random.rst:515
msgid "Simulations::"
msgstr "模擬： ::"

#: ../../library/random.rst:517
msgid ""
">>> # Six roulette wheel spins (weighted sampling with replacement)\n"
">>> choices(['red', 'black', 'green'], [18, 18, 2], k=6)\n"
"['red', 'green', 'black', 'black', 'red', 'black']\n"
"\n"
">>> # Deal 20 cards without replacement from a deck\n"
">>> # of 52 playing cards, and determine the proportion of cards\n"
">>> # with a ten-value:  ten, jack, queen, or king.\n"
">>> deal = sample(['tens', 'low cards'], counts=[16, 36], k=20)\n"
">>> deal.count('tens') / 20\n"
"0.15\n"
"\n"
">>> # Estimate the probability of getting 5 or more heads from 7 spins\n"
">>> # of a biased coin that settles on heads 60% of the time.\n"
">>> sum(binomialvariate(n=7, p=0.6) >= 5 for i in range(10_000)) / 10_000\n"
"0.4169\n"
"\n"
">>> # Probability of the median of 5 samples being in middle two quartiles\n"
">>> def trial():\n"
"...     return 2_500 <= sorted(choices(range(10_000), k=5))[2] < 7_500\n"
"...\n"
">>> sum(trial() for i in range(10_000)) / 10_000\n"
"0.7958"
msgstr ""
">>> # 六次輪盤旋轉（有重置的加權抽樣）\n"
">>> choices(['red', 'black', 'green'], [18, 18, 2], k=6)\n"
"['red', 'green', 'black', 'black', 'red', 'black']\n"
"\n"
">>> # 從一副 52 張撲克牌中無重置發 20 張牌\n"
">>> # 並確定具有十點值的牌的比例：十、傑克、王后或國王\n"
">>> deal = sample(['tens', 'low cards'], counts=[16, 36], k=20)\n"
">>> deal.count('tens') / 20\n"
"0.15\n"
"\n"
">>> # 估計從 7 次旋轉中得到 5 次或更多正面的概率\n"
">>> # 使用一枚 60% 概率為正面的偏幣\n"
">>> sum(binomialvariate(n=7, p=0.6) >= 5 for i in range(10_000)) / 10_000\n"
"0.4169\n"
"\n"
">>> # 計算 5 個樣本的中位數位於中間兩個四分位數的概率\n"
">>> def trial():\n"
"...     return 2_500 <= sorted(choices(range(10_000), k=5))[2] < 7_500\n"
"...\n"
">>> sum(trial() for i in range(10_000)) / 10_000\n"
"0.7958"

#: ../../library/random.rst:540
msgid ""
"Example of `statistical bootstrapping <https://en.wikipedia.org/wiki/"
"Bootstrapping_(statistics)>`_ using resampling with replacement to estimate "
"a confidence interval for the mean of a sample::"
msgstr ""
"`統計 bootstrapping（自助法） <https://en.wikipedia.org/wiki/"
"Bootstrapping_(statistics)>`_\\ 的範例，使用有重置的重新取樣來估計樣本平均數"
"的信賴區間： ::"

#: ../../library/random.rst:544
msgid ""
"# https://www.thoughtco.com/example-of-bootstrapping-3126155\n"
"from statistics import fmean as mean\n"
"from random import choices\n"
"\n"
"data = [41, 50, 29, 37, 81, 30, 73, 63, 20, 35, 68, 22, 60, 31, 95]\n"
"means = sorted(mean(choices(data, k=len(data))) for i in range(100))\n"
"print(f'The sample mean of {mean(data):.1f} has a 90% confidence '\n"
"      f'interval from {means[5]:.1f} to {means[94]:.1f}')"
msgstr ""
"# https://www.thoughtco.com/example-of-bootstrapping-3126155\n"
"from statistics import fmean as mean\n"
"from random import choices\n"
"\n"
"data = [41, 50, 29, 37, 81, 30, 73, 63, 20, 35, 68, 22, 60, 31, 95]\n"
"means = sorted(mean(choices(data, k=len(data))) for i in range(100))\n"
"print(f'The sample mean of {mean(data):.1f} has a 90% confidence '\n"
"      f'interval from {means[5]:.1f} to {means[94]:.1f}')"

#: ../../library/random.rst:553
msgid ""
"Example of a `resampling permutation test <https://en.wikipedia.org/wiki/"
"Resampling_(statistics)#Permutation_tests>`_ to determine the statistical "
"significance or `p-value <https://en.wikipedia.org/wiki/P-value>`_ of an "
"observed difference between the effects of a drug versus a placebo::"
msgstr ""
"`重新取樣排列測試 <https://en.wikipedia.org/wiki/"
"Resampling_(statistics)#Permutation_tests>`_\\ 的範例，來確定觀察到的藥物與安"
"慰劑之間差異的統計學意義或 `p 值 <https://en.wikipedia.org/wiki/P-value>`_\\ "
"： ::"

#: ../../library/random.rst:559
msgid ""
"# Example from \"Statistics is Easy\" by Dennis Shasha and Manda Wilson\n"
"from statistics import fmean as mean\n"
"from random import shuffle\n"
"\n"
"drug = [54, 73, 53, 70, 73, 68, 52, 65, 65]\n"
"placebo = [54, 51, 58, 44, 55, 52, 42, 47, 58, 46]\n"
"observed_diff = mean(drug) - mean(placebo)\n"
"\n"
"n = 10_000\n"
"count = 0\n"
"combined = drug + placebo\n"
"for i in range(n):\n"
"    shuffle(combined)\n"
"    new_diff = mean(combined[:len(drug)]) - mean(combined[len(drug):])\n"
"    count += (new_diff >= observed_diff)\n"
"\n"
"print(f'{n} label reshufflings produced only {count} instances with a "
"difference')\n"
"print(f'at least as extreme as the observed difference of "
"{observed_diff:.1f}.')\n"
"print(f'The one-sided p-value of {count / n:.4f} leads us to reject the "
"null')\n"
"print(f'hypothesis that there is no difference between the drug and the "
"placebo.')"
msgstr ""
"# 範例來自 Dennis Shasha 和 Manda Wilson 的 \"Statistics is Easy\"\n"
"from statistics import fmean as mean\n"
"from random import shuffle\n"
"\n"
"drug = [54, 73, 53, 70, 73, 68, 52, 65, 65]\n"
"placebo = [54, 51, 58, 44, 55, 52, 42, 47, 58, 46]\n"
"observed_diff = mean(drug) - mean(placebo)\n"
"\n"
"n = 10_000\n"
"count = 0\n"
"combined = drug + placebo\n"
"for i in range(n):\n"
"    shuffle(combined)\n"
"    new_diff = mean(combined[:len(drug)]) - mean(combined[len(drug):])\n"
"    count += (new_diff >= observed_diff)\n"
"\n"
"print(f'{n} 次標籤重新洗牌僅產生 {count} 個差異實例')\n"
"print(f'至少與觀察到的差異 {observed_diff:.1f} 一樣極端。')\n"
"print(f'單邊 p 值 {count / n:.4f} 使我們拒絕無效假設')\n"
"print(f'即藥物與安慰劑之間沒有差異。')"

#: ../../library/random.rst:580
msgid ""
"Simulation of arrival times and service deliveries for a multiserver queue::"
msgstr "模擬多伺服器佇列 (queue) 的到達時間與服務交付： ::"

#: ../../library/random.rst:582
msgid ""
"from heapq import heapify, heapreplace\n"
"from random import expovariate, gauss\n"
"from statistics import mean, quantiles\n"
"\n"
"average_arrival_interval = 5.6\n"
"average_service_time = 15.0\n"
"stdev_service_time = 3.5\n"
"num_servers = 3\n"
"\n"
"waits = []\n"
"arrival_time = 0.0\n"
"servers = [0.0] * num_servers  # time when each server becomes available\n"
"heapify(servers)\n"
"for i in range(1_000_000):\n"
"    arrival_time += expovariate(1.0 / average_arrival_interval)\n"
"    next_server_available = servers[0]\n"
"    wait = max(0.0, next_server_available - arrival_time)\n"
"    waits.append(wait)\n"
"    service_duration = max(0.0, gauss(average_service_time, "
"stdev_service_time))\n"
"    service_completed = arrival_time + wait + service_duration\n"
"    heapreplace(servers, service_completed)\n"
"\n"
"print(f'Mean wait: {mean(waits):.1f}   Max wait: {max(waits):.1f}')\n"
"print('Quartiles:', [round(q, 1) for q in quantiles(waits)])"
msgstr ""
"from heapq import heapify, heapreplace\n"
"from random import expovariate, gauss\n"
"from statistics import mean, quantiles\n"
"\n"
"average_arrival_interval = 5.6\n"
"average_service_time = 15.0\n"
"stdev_service_time = 3.5\n"
"num_servers = 3\n"
"\n"
"waits = []\n"
"arrival_time = 0.0\n"
"servers = [0.0] * num_servers  # 每個伺服器可用的時間\n"
"heapify(servers)\n"
"for i in range(1_000_000):\n"
"    arrival_time += expovariate(1.0 / average_arrival_interval)\n"
"    next_server_available = servers[0]\n"
"    wait = max(0.0, next_server_available - arrival_time)\n"
"    waits.append(wait)\n"
"    service_duration = max(0.0, gauss(average_service_time, "
"stdev_service_time))\n"
"    service_completed = arrival_time + wait + service_duration\n"
"    heapreplace(servers, service_completed)\n"
"\n"
"print(f'平均等待時間：{mean(waits):.1f}   最大等待時間：{max(waits):.1f}')\n"
"print('四分位數：', [round(q, 1) for q in quantiles(waits)])"

#: ../../library/random.rst:609
msgid ""
"`Statistics for Hackers <https://www.youtube.com/watch?v=Iq9DzN6mvYA>`_ a "
"video tutorial by `Jake Vanderplas <https://us.pycon.org/2016/speaker/"
"profile/295/>`_ on statistical analysis using just a few fundamental "
"concepts including simulation, sampling, shuffling, and cross-validation."
msgstr ""
"`Statistics for Hackers <https://www.youtube.com/watch?v=Iq9DzN6mvYA>`_ 是由 "
"`Jake Vanderplas <https://us.pycon.org/2016/speaker/profile/295/>`_ 製作的教"
"學影片，僅使用幾個基本概念（包括模擬、取樣、洗牌、交叉驗證）進行統計分析。"

#: ../../library/random.rst:615
msgid ""
"`Economics Simulation <https://nbviewer.org/url/norvig.com/ipython/Economics."
"ipynb>`_ a simulation of a marketplace by `Peter Norvig <https://norvig.com/"
"bio.html>`_ that shows effective use of many of the tools and distributions "
"provided by this module (gauss, uniform, sample, betavariate, choice, "
"triangular, and randrange)."
msgstr ""
"`Economics Simulation <https://nbviewer.org/url/norvig.com/ipython/Economics."
"ipynb>`_\\ 是由 `Peter Norvig <https://norvig.com/bio.html>`_ 對市場進行的模"
"擬，顯示了該模組提供的許多工具和分佈（高斯、均勻、樣本、 beta 變數、選擇，三"
"角形、隨機數）的有效使用。"

#: ../../library/random.rst:622
msgid ""
"`A Concrete Introduction to Probability (using Python) <https://nbviewer.org/"
"url/norvig.com/ipython/Probability.ipynb>`_ a tutorial by `Peter Norvig "
"<https://norvig.com/bio.html>`_ covering the basics of probability theory, "
"how to write simulations, and how to perform data analysis using Python."
msgstr ""
"`機率的具體介紹（使用Python） <https://nbviewer.org/url/norvig.com/ipython/"
"Probability.ipynb>`_\\ 為 `Peter Norvig <https://norvig.com/bio.html>`_ 的教"
"學課程，涵蓋了機率理論的基礎知識與如何模擬以及使用 Python 執行數據分析。"

#: ../../library/random.rst:630
msgid "Recipes"
msgstr "使用方案"

#: ../../library/random.rst:632
msgid ""
"These recipes show how to efficiently make random selections from the "
"combinatoric iterators in the :mod:`itertools` module:"
msgstr ""
"這些使用方案展示了如何有效地從 :mod:`itertools` 模組的組合疊代器 "
"(combinatoric iterators) 中進行隨機選擇："

#: ../../library/random.rst:635
msgid ""
"def random_product(*args, repeat=1):\n"
"    \"Random selection from itertools.product(*args, **kwds)\"\n"
"    pools = [tuple(pool) for pool in args] * repeat\n"
"    return tuple(map(random.choice, pools))\n"
"\n"
"def random_permutation(iterable, r=None):\n"
"    \"Random selection from itertools.permutations(iterable, r)\"\n"
"    pool = tuple(iterable)\n"
"    r = len(pool) if r is None else r\n"
"    return tuple(random.sample(pool, r))\n"
"\n"
"def random_combination(iterable, r):\n"
"    \"Random selection from itertools.combinations(iterable, r)\"\n"
"    pool = tuple(iterable)\n"
"    n = len(pool)\n"
"    indices = sorted(random.sample(range(n), r))\n"
"    return tuple(pool[i] for i in indices)\n"
"\n"
"def random_combination_with_replacement(iterable, r):\n"
"    \"Choose r elements with replacement.  Order the result to match the "
"iterable.\"\n"
"    # Result will be in set(itertools."
"combinations_with_replacement(iterable, r)).\n"
"    pool = tuple(iterable)\n"
"    n = len(pool)\n"
"    indices = sorted(random.choices(range(n), k=r))\n"
"    return tuple(pool[i] for i in indices)"
msgstr ""
"def random_product(*args, repeat=1):\n"
"    \"從 itertools.product(*args, **kwds) 中隨機選擇\"\n"
"    pools = [tuple(pool) for pool in args] * repeat\n"
"    return tuple(map(random.choice, pools))\n"
"\n"
"def random_permutation(iterable, r=None):\n"
"    \"從 itertools.permutations(iterable, r) 中隨機選擇\"\n"
"    pool = tuple(iterable)\n"
"    r = len(pool) if r is None else r\n"
"    return tuple(random.sample(pool, r))\n"
"\n"
"def random_combination(iterable, r):\n"
"    \"從 itertools.combinations(iterable, r) 中隨機選擇\"\n"
"    pool = tuple(iterable)\n"
"    n = len(pool)\n"
"    indices = sorted(random.sample(range(n), r))\n"
"    return tuple(pool[i] for i in indices)\n"
"\n"
"def random_combination_with_replacement(iterable, r):\n"
"    \"有重置地選擇 r 個元素。結果按可疊代物件排序。\"\n"
"    # 結果將在 set(itertools.combinations_with_replacement(iterable, r)) 中\n"
"    pool = tuple(iterable)\n"
"    n = len(pool)\n"
"    indices = sorted(random.choices(range(n), k=r))\n"
"    return tuple(pool[i] for i in indices)"

#: ../../library/random.rst:664
msgid ""
"The default :func:`.random` returns multiples of 2⁻⁵³ in the range *0.0 ≤ x "
"< 1.0*.  All such numbers are evenly spaced and are exactly representable as "
"Python floats.  However, many other representable floats in that interval "
"are not possible selections.  For example, ``0.05954861408025609`` isn't an "
"integer multiple of 2⁻⁵³."
msgstr ""
"預設的 :func:`.random` 回傳 *0.0 ≤ x < 1.0* 範圍內 2⁻⁵³ 的倍數。所有數字都是"
"均勻分佈的，並且可以完全表示為 Python float。但是，該間隔中的許多其他可表示"
"的 float 不是可能的選擇。 例如 ``0.05954861408025609`` 不是 2⁻⁵³ 的整數倍。"

#: ../../library/random.rst:670
msgid ""
"The following recipe takes a different approach.  All floats in the interval "
"are possible selections.  The mantissa comes from a uniform distribution of "
"integers in the range *2⁵² ≤ mantissa < 2⁵³*.  The exponent comes from a "
"geometric distribution where exponents smaller than *-53* occur half as "
"often as the next larger exponent."
msgstr ""
"以下範例採用不同的方法。間隔中的所有 float 都是可能的選擇。尾數來自 *2⁵² ≤ 尾"
"數 < 2⁵³* 範圍內的整數均勻分佈。指數來自幾何分佈，其中小於 *-53* 的指數的出現"
"頻率是下一個較大指數的一半。"

#: ../../library/random.rst:678
msgid ""
"from random import Random\n"
"from math import ldexp\n"
"\n"
"class FullRandom(Random):\n"
"\n"
"    def random(self):\n"
"        mantissa = 0x10_0000_0000_0000 | self.getrandbits(52)\n"
"        exponent = -53\n"
"        x = 0\n"
"        while not x:\n"
"            x = self.getrandbits(32)\n"
"            exponent += x.bit_length() - 32\n"
"        return ldexp(mantissa, exponent)"
msgstr ""
"from random import Random\n"
"from math import ldexp\n"
"\n"
"class FullRandom(Random):\n"
"\n"
"    def random(self):\n"
"        mantissa = 0x10_0000_0000_0000 | self.getrandbits(52)\n"
"        exponent = -53\n"
"        x = 0\n"
"        while not x:\n"
"            x = self.getrandbits(32)\n"
"            exponent += x.bit_length() - 32\n"
"        return ldexp(mantissa, exponent)"

#: ../../library/random.rst:692
msgid ""
"All :ref:`real valued distributions <real-valued-distributions>` in the "
"class will use the new method::"
msgstr ""
"Class 中的所有\\ :ref:`實數分佈 <real-valued-distributions>`\\ 都將使用新方"
"法： ::"

#: ../../library/random.rst:695
msgid ""
">>> fr = FullRandom()\n"
">>> fr.random()\n"
"0.05954861408025609\n"
">>> fr.expovariate(0.25)\n"
"8.87925541791544"
msgstr ""
">>> fr = FullRandom()\n"
">>> fr.random()\n"
"0.05954861408025609\n"
">>> fr.expovariate(0.25)\n"
"8.87925541791544"

#: ../../library/random.rst:701
msgid ""
"The recipe is conceptually equivalent to an algorithm that chooses from all "
"the multiples of 2⁻¹⁰⁷⁴ in the range *0.0 ≤ x < 1.0*.  All such numbers are "
"evenly spaced, but most have to be rounded down to the nearest representable "
"Python float.  (The value 2⁻¹⁰⁷⁴ is the smallest positive unnormalized float "
"and is equal to ``math.ulp(0.0)``.)"
msgstr ""
"該範例在概念上等效於一種演算法，該演算法從 *0.0 ≤ x < 1.0* 範圍內 2⁻¹⁰⁷⁴ 的所"
"有倍數中進行選擇。這些數字都是均勻分佈的，但大多數必須向下捨入到最接近的可表"
"示的 Python float。（2⁻¹⁰⁷⁴ 是最小為正的非正規化 float，等於 ``math."
"ulp(0.0)``）"

#: ../../library/random.rst:710
msgid ""
"`Generating Pseudo-random Floating-Point Values <https://allendowney.com/"
"research/rand/downey07randfloat.pdf>`_ a paper by Allen B. Downey describing "
"ways to generate more fine-grained floats than normally generated by :func:`."
"random`."
msgstr ""
"`產生偽隨機浮點值 <https://allendowney.com/research/rand/downey07randfloat."
"pdf>`_  Allen B. Downey 的一篇論文描述了產生比通常由 :func:`.random` 產生的 "
"float 更 fine-grained（細粒的）的方法。"

#: ../../library/random.rst:718
msgid "Command-line usage"
msgstr "命令列用法"

#: ../../library/random.rst:722
msgid "The :mod:`!random` module can be executed from the command line."
msgstr ":mod:`!random` 模組可以從命令列執行。"

#: ../../library/random.rst:724
msgid ""
"python -m random [-h] [-c CHOICE [CHOICE ...] | -i N | -f N] [input ...]"
msgstr ""
"python -m random [-h] [-c CHOICE [CHOICE ...] | -i N | -f N] [input ...]"

#: ../../library/random.rst:728
msgid "The following options are accepted:"
msgstr "接受以下選項："

#: ../../library/random.rst:734
msgid "Show the help message and exit."
msgstr "顯示幫助訊息並退出。"

#: ../../library/random.rst:739
msgid "Print a random choice, using :meth:`choice`."
msgstr "列印一個隨機選擇，使用 :meth:`choice`。"

#: ../../library/random.rst:744
msgid ""
"Print a random integer between 1 and N inclusive, using :meth:`randint`."
msgstr "列印 1 到 N（含）之間的隨機整數，使用 :meth:`randint`。"

#: ../../library/random.rst:749
msgid ""
"Print a random floating-point number between 0 and N inclusive, using :meth:"
"`uniform`."
msgstr "列印 0 到 N（含）之間的隨機浮點數，使用 :meth:`uniform`。"

#: ../../library/random.rst:752
msgid "If no options are given, the output depends on the input:"
msgstr "如果未給定選項，則輸出取決於輸入："

#: ../../library/random.rst:754
msgid "String or multiple: same as :option:`--choice`."
msgstr "字串或多個：與 :option:`--choice` 相同。"

#: ../../library/random.rst:755
msgid "Integer: same as :option:`--integer`."
msgstr "整數：與 :option:`--integer` 相同。"

#: ../../library/random.rst:756
msgid "Float: same as :option:`--float`."
msgstr "浮點數：與 :option:`--float` 相同。"

#: ../../library/random.rst:761
msgid "Command-line example"
msgstr "命令列範例"

#: ../../library/random.rst:763
msgid "Here are some examples of the :mod:`!random` command-line interface:"
msgstr "以下是 :mod:`!random` 命令列介面的一些範例："

#: ../../library/random.rst:765
msgid ""
"$ # Choose one at random\n"
"$ python -m random egg bacon sausage spam \"Lobster Thermidor aux crevettes "
"with a Mornay sauce\"\n"
"Lobster Thermidor aux crevettes with a Mornay sauce\n"
"\n"
"$ # Random integer\n"
"$ python -m random 6\n"
"6\n"
"\n"
"$ # Random floating-point number\n"
"$ python -m random 1.8\n"
"1.7080016272295635\n"
"\n"
"$ # With explicit arguments\n"
"$ python  -m random --choice egg bacon sausage spam \"Lobster Thermidor aux "
"crevettes with a Mornay sauce\"\n"
"egg\n"
"\n"
"$ python -m random --integer 6\n"
"3\n"
"\n"
"$ python -m random --float 1.8\n"
"1.5666339105010318\n"
"\n"
"$ python -m random --integer 6\n"
"5\n"
"\n"
"$ python -m random --float 6\n"
"3.1942323316565915"
msgstr ""
"$ # 隨機選擇一個\n"
"$ python -m random egg bacon sausage spam \"Lobster Thermidor aux crevettes "
"with a Mornay sauce\"\n"
"Lobster Thermidor aux crevettes with a Mornay sauce\n"
"\n"
"$ # 隨機整數\n"
"$ python -m random 6\n"
"6\n"
"\n"
"$ # 隨機浮點數\n"
"$ python -m random 1.8\n"
"1.7080016272295635\n"
"\n"
"$ # 使用明確的引數\n"
"$ python  -m random --choice egg bacon sausage spam \"Lobster Thermidor aux "
"crevettes with a Mornay sauce\"\n"
"egg\n"
"\n"
"$ python -m random --integer 6\n"
"3\n"
"\n"
"$ python -m random --float 1.8\n"
"1.5666339105010318\n"
"\n"
"$ python -m random --integer 6\n"
"5\n"
"\n"
"$ python -m random --float 6\n"
"3.1942323316565915"