第1个回答 2011-08-15
必须说明一点,K不可能取值0,所以累加应该是从K=(1->+∞)
令S(x)=∑k²(1-x)x^(k-1) |x|<1
S(x)=(1-x)∑k²x^(k-1)
=(1-x)∑[kx^k]'
=(1-x)[x∑kx^(k-1)]'
=(1-x)[x∑[x^k]']'
=(1-x)[x[∑x^k]']'
=(1-x)[x[x/(1-x)]']'
=(1-x)[x/(1-x)²]'
=(1+x)/(1-x)²
E(X^2)=S(q)=S(1-p)=(2-p)/p²=(1+q)/p²
比较简单的方法:
EX²=DX+(EX)²=q/p²+1/p²=(1+q)/p²