zoukankan      html  css  js  c++  java
  • 几何分布

    定义

    [P(X = k) = q^{k - 1}p, quad k = 1,2,..., 0 < p < 1, q = 1 - p, ]

    记为 (X sim G(p)).

    期望

    [EX = frac{1}{p}. ]

    证明

    [EX = sum_{k = 1}^{infty }kq^{k - 1}p = psum_{k = 1}^{infty }kq^{k - 1} = psum_{k = 1}^{infty }frac{dq^{k}}{dq} = p cdot frac{ddisplaystyle sum_{k = 1}^{infty }q^{k}}{dq} = p cdot frac{d displaystyle frac{q}{1 - q}}{dq} = frac{p}{(1 - q)^2}, ]

    所以,

    [EX = frac{1}{p}. ]

    方差

    [DX = frac{1 - p}{p^2}. ]

  • 相关阅读:
    CF1037H
    CF1296F
    CF1446F
    CF1175G
    CF1146G
    CF1303G
    CF1067D
    CF1477E
    COJ16G
    ZJOI2018 迷宫
  • 原文地址:https://www.cnblogs.com/fanlumaster/p/14022535.html
Copyright © 2011-2022 走看看