Probability and Statistics

Which of the following statements are TRUE for any two random variables $X$ and $Y$?

Options:

• (A) $E[X + Y] = E[X] + E[Y]$ (linearity of expectation holds always)
• (B) $\text{Var}(X + Y) = \text{Var}(X) + \text{Var}(Y) + 2\text{Cov}(X, Y)$
• (C) If $\text{Cov}(X, Y) = 0$, $X$ and $Y$ must always be strictly independent
• (D) $-1 \le \text{Corr}(X, Y) \le 1$