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好吧问答库 > 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X服从泊松分布,且P(X<=1)=4P(X=2),则P(X=3)=?

2025年04月03日 01:18

有3个网友回答

网友（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

网友（2）：

1/6e^(-1)

网友（3）：

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

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