Question
Two probability distributions of the discrete random variable X and Y are given below.
Prove that E(Y2) = 2E(X).
| $\text{X}$ | $0$ | $1$ | $2$ | $3$ |
| $\text{P}(\text{X})$ | $\frac{1}{5}$ | $\frac{2}{5}$ | $\frac{1}{5}$ | $\frac{1}{5}$ |
| $\text{Y}$ | $0$ | $1$ | $2$ | $3$ |
| $\text{P}(\text{Y})$ | $\frac{1}{5}$ | $\frac{3}{10}$ | $\frac{2}{5}$ | $\frac{1}{10}$ |