概率与数理统计的题目，麻烦了啊

Question

设X～B(10,0.4)
则E(X~2)= ?
括号为X的2次方

Answer 1

因为 X ～ B(10,0.4) ,
所以 E(X) = 10 * 0.4 = 4 , D(X) = 10 * 0.4 * (1 - 0.4) = 2.4 ,
因为
D(X) = E{ [X - E(X)]^2 } = E{ X^2 - 2 X E(X) + [E(X)]^2 }
= E(X^2) - 2 E(X) E(X) + [E(X)]^2 = E(X^2) - [E(X)]^2 ,
所以 E(X^2) = D(X) + [E(X)]^2 ,
所以 E(X^2) = D(X) + [E(X)]^2 = 2.4 + 4^2 = 18.4 .

Answer 2

由x服从伯努利分布，n=10,p=0.4
E（x)=np=4
Var(x)=np(1-p)=2.4=E(x^2）-[E(x)]^2

所以E(x^2)=18.4

Answer 3

DX=E(X^2)-(EX)^2 DX=np(1-p)=10*0.4*0.6=2.4 EX=np=10*0.4=4
所以E(X^2)=18.4

Answer 4

E(x^2)=D(x)+(E(x))^2
D(x)=npq=10*0.4*0.6=2.4
E(x)=np=10*0.4=4
E(x^2)=2.4+4^2=18.4本回答被提问者采纳