Question

设X是随机变量,C是常数,D(X)存在,试证：对于任意C≠E(X)必有E(X-C)^2＞D(X).(上式表明E(X-C)

Answer 1

E(X-C)^2-D(X)=E(X^2-2CX+C^2)-(EX^2-(EX)^2)=(EX)^2-2C(EX)+C^2>=0