设随机变量X的分布律P{X=K}=C/K!,K=0,1,2.则X的平方的期望是多少?

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设随机变量X的分布律P{X=K}=C/K!,K=0,1,2.则X的平方的期望是多少?
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设随机变量X的分布律P{X=K}=C/K!,K=0,1,2.则X的平方的期望是多少?
设随机变量X的分布律P{X=K}=C/K!,K=0,1,2.则X的平方的期望是多少?

设随机变量X的分布律P{X=K}=C/K!,K=0,1,2.则X的平方的期望是多少?
1=Sum(k=0->无穷大)C/k!=C*Sum(k=0->无穷大)[1/k!]=C*e,C = 1/e.
E[x^2]=C*Sum(k=0->无穷大)k^2/k!=C*Sum(k=1->无穷大)k^2/k!=C*Sum(k=1->无穷大)k/(k-1)!=C*Sum(k=1->无穷大)(k-1+1)/(k-1)!
=C*Sum(k=1->无穷大)(k-1)/(k-1)!+ C*Sum(k=1->无穷大)1/(k-1)!
=C*Sum(k=2->无穷大)1/(k-2)!+ C*Sum(k=1->无穷大)1/(k-1)!
=C*(1/e) + C*(1/e)
=2C/e
=2