Question

Which is larger: the expectation of the square of a random variable, or the squareof its expectation?

Answer 1

Since p is a fraction it is greater than p^2. So (x^2){p - p^2} is positive. Summing over all variables we get by definition E[X^2] - (E[X])^2 >= 0 or E[X^2] >= (E[X])^2. Taking square root and putting X = X^0•5 gives us the result. Since probability is a fraction and becomes very small as number of variables are large summing ..