求E(X^2)的期望,其中P(x=k)=p(1-p)^(k-1) k=1,2,3……
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求E(X^2)的期望,其中P(x=k)=p(1-p)^(k-1) k=1,2,3……
求E(X^2)的期望,其中P(x=k)=p(1-p)^(k-1) k=1,2,3……
求E(X^2)的期望,其中P(x=k)=p(1-p)^(k-1) k=1,2,3……
E(x^2)=∑x^2p(x=k)=0*p(1-p)^0+1*p(1-p)^1+2*p(1-p)^2+...+np(1-p)^n+..
=1*p(1-p)^1+2*p(1-p)^2+...+np(1-p)^n+..①
(1-p)E(x^2)= 1*p(1-p)^2+...+(n-1)p(1-p)^n+...②
①-②:pE(x^2)=p(1-p)+p*(1-p)^2+.+p(1-p)^n+...
x取遍1,2,3,.其概率和是1,即∑p(x=k)=p(1-p)^0+p(1-p)^1+p(1-p)^2+.=1
所以,pE(x^2)=1 -->E(x^2)=1/p