Two probability distributions of the discrete random variable X and Y are given below.

Question

  X 0 1 2 3 P(X) $\frac{1}{5}$ $\frac{2}{5}$ $\frac{1}{5}$ $\frac{1}{5}$ Y 0 1 2 3 P(Y) $\frac{1}{5}$ $\frac{3}{10}$ $\frac{2}{5}$ $\frac{1}{10}$ Prove that $E(Y^2)=2E(X)$.