1. The problem statement, all variables and given/known data Given a square with side lengths X, where X is a random variable with some probability density function (the actual pdf is not important for my question). Why isn't the expected value of the area = E[X]^2 = E[X^2]? 2. Relevant equations 3. The attempt at a solution Intuitively I would think, if I can find the expected value of one of the sides, I can get the expected value of the area by squaring it. On the other hand, I am well aware that E[X]^2 != E[X^2] in the general case, and this is indeed a general case (with some geometric interpretation).