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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク geometric distribution ： ウィキペディア英語版 geometric distribution \! | kurtosis = $6+\backslash frac\backslash !$ | entropy = $\backslash tfrac\backslash !$ | mgf = $\backslash frac\backslash !$, for | char = $\backslash frac\}\backslash !$ | parameters2 = success probability (real) | support2 = k failures where $k\; \backslash in\; \backslash \backslash !$ | pdf2 = $(1\; -\; p)^\backslash ,p\backslash !$ | cdf2 = $1-(1\; -\; p)^\backslash !$ | mean2 = $\backslash frac\backslash !$ | median2 = $\backslash left\backslash lceil\; \backslash frac\; \backslash right\backslash rceil\backslash !\; -\; 1$ (not unique if $-1/\backslash log\_2(1-p)$ is an integer) | mode2 = $0$ | variance2 = $\backslash frac\backslash !$ | skewness2 = $\backslash frac\backslash !$ | entropy2 = $\backslash tfrac\backslash !$ | mgf2 = $\backslash frac\backslash !$ | char2 = $\backslash frac\}$ In probability theory and statistics, the geometric distribution is either of two discrete probability distributions: * The probability distribution of the number ''X'' of Bernoulli trials needed to get one success, supported on the set  * The probability distribution of the number ''Y'' = ''X'' − 1 of failures before the first success, supported on the set  Which of these one calls "the" geometric distribution is a matter of convention and convenience. These two different geometric distributions should not be confused with each other. Often, the name ''shifted'' geometric distribution is adopted for the former one (distribution of the number ''X''); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly. It’s the probability that the first occurrence of success requires ''k'' number of independent trials, each with success probability p. If the probability of success on each trial is ''p'', then the probability that the ''k''th trial (out of ''k'' trials) is the first success is :$\backslash Pr(X\; =\; k)\; =\; (1-p)^\backslash ,p\backslash ,$ for ''k'' = 1, 2, 3, .... The above form of geometric distribution is used for modeling the number of trials up to and including the first success. By contrast, the following form of the geometric distribution is used for modeling the number of failures until the first success: :$\backslash Pr(Y=k)\; =\; (1\; -\; p)^k\backslash ,p\backslash ,$ for ''k'' = 0, 1, 2, 3, .... In either case, the sequence of probabilities is a geometric sequence. For example, suppose an ordinary die is thrown repeatedly until the first time a "1" appears. The probability distribution of the number of times it is thrown is supported on the infinite set and is a geometric distribution with ''p'' = 1/6. ==Introduction to the geometric distribution== Consider a sequence of trials, where each trial has only two possible outcomes (designated failure and success). The probability of success is assumed to be the same for each trial. In such a sequence of trials, the geometric distribution is useful to model the number of failures before the first success. The distribution gives the probability that there are zero failures before the first success, one failure before the first success, two failures before the first success, and so on. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「geometric distribution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.