设随机变量X服从参数λ的泊松分布,且P{X=0}=1⼀2,求P{X>1﹜

2025-04-08 13:16:42
推荐回答(3个)
回答1:

F(x)=λ^ke^(-λ)/k!
由P{X=0}=1/2得
e^(-λ)=1/2
λ=ln2
则F(x)=(ln2)^k/2(k!)
P{X>1}=1-P{X<=1}=1-P{X=1}-P{X=0}=1-(ln2)/2-1/2=1/2-(ln2)/2

回答2:

解:P{X=0}=(λ^0/0!)×e^-λ=1/2,解得λ=ln2,P{X>1﹜=1-P{X=0}-P{X=1}=1/2-P{X=1}=1/2-(λ^1/1!)×e^-λ=1/2(1-ln2)

回答3:

p{x=0}=1/2 ---> lamda=ln2---> p{x>1}=1-p{x<=1}=1-p(0)-p(1)=0.5(1-ln2)=0.15342640972003