【30分】求解一道概率题目
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【30分】求解一道概率题目
不好意思,刚刚忘了写题目了,hoho
设随机变量§的分布律为:
§ -1 0 1/2 1 2
概率 1/3 1/6 1/6 1/12 1/4
求(1)E(§) ;(2) E(§^2)[指§的平方] ;(3)D(§)
不好意思,刚刚忘了写题目了,hoho
设随机变量§的分布律为:
§ -1 0 1/2 1 2
概率 1/3 1/6 1/6 1/12 1/4
求(1)E(§) ;(2) E(§^2)[指§的平方] ;(3)D(§)
E(§) = -1*(1/3) + 1/2*(1/6) + 1*(1/12) + 2*(1/4)
= -1/3 + 1/12 + 1/12 + 1/2
= 1/3
E(§^2) = (-1)^2*(1/3) + (1/2)^2*(1/6) + 1^2*(1/12) + 2^2*(1/4)
= 1/3 + 1/24 + 1/12 + 1
= (8+1+2+24)/24
= 35/24
D(§) = E(§^2) - [E(§)]^2
= 35/24 - (1/3)^2
= 35/24 - 1/9
= (35*3 - 8)/(3*24)
= 97/72
= -1/3 + 1/12 + 1/12 + 1/2
= 1/3
E(§^2) = (-1)^2*(1/3) + (1/2)^2*(1/6) + 1^2*(1/12) + 2^2*(1/4)
= 1/3 + 1/24 + 1/12 + 1
= (8+1+2+24)/24
= 35/24
D(§) = E(§^2) - [E(§)]^2
= 35/24 - (1/3)^2
= 35/24 - 1/9
= (35*3 - 8)/(3*24)
= 97/72