设随机变量x~b(5,p),且p{x=2}=p{x=3},求p{x=k}=?,k=0,1,2,3,4,5

题目

设随机变量x~b(5,p),且p{x=2}=p{x=3},求p{x=k}=?,k=0,1,2,3,4,5

答案

由p{x=2}=p{x=3}
得λ^2/2!*e^(-λ)=λ^3/3!*e^(-λ)
λ=3
故p{x=k}=λ^k/k!*e^(-λ)(k=0,1,2,...)