翻訳と辞書 Words near each other ・ Bernolákovo ・ Bernon ・ Bernon Worsted Mill ・ Bernos ・ Bernos-Beaulac ・ Bernot ・ Bernot (disambiguation) ・ Bernot, Aisne ・ Bernotas ・ Bernouil ・ Bernouilli Conservation Reserve ・ Bernoulli ・ Bernoulli (crater) ・ Bernoulli Box ・ Bernoulli differential equation ・ Bernoulli distribution ・ Bernoulli equation ・ Bernoulli family ・ Bernoulli grip ・ Bernoulli number ・ Bernoulli polynomials ・ Bernoulli process ・ Bernoulli sampling ・ Bernoulli scheme ・ Bernoulli Society for Mathematical Statistics and Probability ・ Bernoulli space ・ Bernoulli stochastics ・ Bernoulli trial ・ Bernoulli's inequality ・ Bernoulli's principle Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bernoulli distribution ： ウィキペディア英語版 Bernoulli distribution | kurtosis =$\backslash frac$| entropy =$-q\backslash ln(q)-p\backslash ln(p)\backslash ,$| mgf =$q+pe^t\backslash ,$| char =$q+pe^\backslash ,$| pgf =$q+pz\backslash ,$| fisher = $\backslash frac$| }} In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jacob Bernoulli,〔James Victor Uspensky: ''Introduction to Mathematical Probability'', McGraw-Hill, New York 1937, page 45〕 is the probability distribution of a random variable which takes the value 1 with success probability of $p$ and the value 0 with failure probability of $q=1-p$. It can be used to represent a coin toss where 1 and 0 would represent "head" and "tail" (or vice versa), respectively. In particular, unfair coins would have $p\; \backslash neq\; 0.5$. The Bernoulli distribution is a special case of the two-point distribution, for which the two possible outcomes need not be 0 and 1. ==Properties== If $X$ is a random variable with this distribution, we have: :$Pr(X=1)\; =\; 1\; -\; Pr(X=0)\; =\; 1\; -\; q\; =\; p.\backslash !$ The probability mass function $f$ of this distribution, over possible outcomes ''k'', is : 1-p & \text k=0.\end This can also be expressed as :$f(k;p)\; =\; p^k\; (1-p)^\backslash !\backslash quad\; \backslash textk\backslash in\backslash .$ The Bernoulli distribution is a special case of the binomial distribution with $n\; =\; 1$.〔McCullagh and Nelder (1989), Section 4.2.2.〕 The kurtosis goes to infinity for high and low values of $p$, but for $p=1/2$ the two-point distributions including the Bernoulli distribution have a lower excess kurtosis than any other probability distribution, namely −2. The Bernoulli distributions for $0\; \backslash le\; p\; \backslash le\; 1$ form an exponential family. The maximum likelihood estimator of $p$ based on a random sample is the sample mean. 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「Bernoulli 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.