设离散型随机变量X的概率分布为P（X=n）=ap的n次方,n=0,1,2.而且X取奇数值得概率为3/7,试求常数a,p的值.

Question

设离散型随机变量X的概率分布为 P（X=n）=ap的n次方,n=0,1,2.而且X取奇数值得概率为3/7,试求常数a,p的值.

Answer 1

P(X=奇数) = ap+ap^3+ap^5+...= ap/(1-p^2) = 3/7 ---(1)
P(X=偶数) = a+ap^2+ap^4+...= a/(1-p^2)
P(X=奇数)+P(X=偶数)=1
ap(1/1-p^2)+a(1/1-p^2)=1 --> a = 1-p --- (2)
由式(1),(2)得:p=3/4,a=1/4.