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?](/uploads/image/z/6867650-2-0.jpg?t=%E8%AE%BE%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8FX%E7%9A%84%E5%88%86%E5%B8%83%E5%BE%8BP%7BX%3DK%7D%3DC%2FK%21%2CK%3D0%2C1%2C2.%E5%88%99X%E7%9A%84%E5%B9%B3%E6%96%B9%E7%9A%84%E6%9C%9F%E6%9C%9B%E6%98%AF%E5%A4%9A%E5%B0%91%3F)
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