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@ynakayama

離散型確率分布

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覚書です。

離散型の確率分布

離散一様分布

確率変数 X が 1,2, ... ,n をとるとするとき

P(X = x) = \frac 1 n \\
(x = 1,...,n)

このとき平均と分散はそれぞれ (n+1)/2 及び (n^2-1)/2 。

ベルヌーイ分布

確率変数 X が 0 または 1 のとき

P(X = x) = p^x(1-p)^{1-x} \\
(x = 0, 1)

このとき平均と分散はそれぞれ p 及び p(1-p)

二項分布

B(n, p)

ポアソン分布

P(X = x) = exp(-\lambda)\frac {\lambda^x} {x!} \\
(x = 0,1, ...)

期待値及び分散が等しくなる (E[X] = Var[X] = λ)

幾何分布

P(X = x) = p(1 - p)^x \\
(x = 0,1, ...)

他にもありますが省略します。

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ynakayama
Software Engineer
dts
コンサルティングから設計、開発、HW/SWの選定、運用、保守までシステムをサポートする総合情報サービス企業です。

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