Question

设随机变量X服从泊松分布,且P(X<=1)=4P(X=2),则P(X=3)=?

设随机变量服X服从泊松分布,且P(X<=1)=4P(X=2),则P(X=3)=?
哪位高手帮忙回答！！

Answer 1

p(X=1)+p(X=0)=4P(X=2)e^(-λ）+λe^(-λ)=4 λ^2 e^(-λ)/2!2λ^2-λ-1=0 λ=3P(X=3)=λ^3 e^(-λ)/3!=9/2 e^-3

Answer 2

1/6e^(-1)

Answer 3

P(X=3)=e^(-1)/6