Question

设离散型随机变量X满足EX=-1,DX=3,则E[3(X^-2)]为多少

Answer 1

D(x)=E(x^2)-(Ex)^2

E(x^2)=D(x)+(Ex)^2

E[(3x-2)^2]=9E(x^2)-12E(x)+4=9(D(x)+(E(x))^2)-12E(x)+4=9(3+1)+12+4=52;