题目

1、盒中有9个正品和3个废品,每次取一个产品,取出后不再收回,在取得正品前已取出的废品数∮的期望E∮是多少?
2、罐中有6个红球,4个白球,从中任取1球,记住球的颜色再放回,连续摸取4次,设∮为取得红球的次数,则∮的期望E∮是多少?

提问时间：2020-10-20

答案

概率C(∮) = (3P∮ * 9P1)/(12P(∮+1))
C(0) = 9/12
C(1) = 3/12 * 9/11
C(2) = 3/12 * 2/11 * 9/10
C(3) = 3/12 * 2/11 * 1/10
E(∮) = 1*C(1) + 2*C(2) + 3*C(3)
= 0.3
概率C(∮) = 4C∮ * 0.4^(4-∮) * 0.6^∮
C(0) = 4C0 * 0.4^4
C(1) = 4C1 * 0.4)^3 * (0.6)
C(2) = 4C2 * 0.4^2 * (0.6)^2
C(3) = 4C3 * 0.4 * (0.6)^3
C(4) = 4C4 * 0.6^4
E(∮) = 1*C(1) + 2*C(2) + 3*C(3) + 4*C(4)
= 2.4