::已知X服从两点分布,求证:DX
问题描述:
::已知X服从两点分布,求证:DX
答
设分布是p(x)=a,p(y)=b;
则a+b=1,EX=xa+yb
DX=a*(x-xa-yb)^2+b*(y-xa-yb)^2=(ab^2+ba^2)(x-y)^2=(a+b)ab(x-y)^2