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62问答网 > 设随机变量X服从泊松分布,且已知P(X=1)=P(X=2),则F(X=3)=，求详解，谢谢！

设随机变量X服从泊松分布,且已知P(X=1)=P(X=2),则F(X=3)=，求详解，谢谢！

2025-04-08 09:15:19

推荐回答（2个）

回答1：

由题 P(X=1)=，P(X=2)=，P(X=1)=P(X=2)，可得=0或2（0舍去），则=2，

F（X=3）=P（X=3）=P(X=0）+P(X=1)+P(X=2)+P(X=3)=0.1353+0.2706+0.2706+0.1804=0.8569

回答2：

解：P(X=1)=ne^（-n）
P(X=2)=n^2e^(-n)/2
得到1=n/2
n=2
X~P(2)
P(X=3)=n^3 e^(-n) /3!=(4/3)e^(-2)
如有意见，欢迎讨论，共同学习；如有帮助，请选为满意回答！

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