Question

Let $X$ and $Y$ be independent random variables having $\text{Bin}(18, 0.5)$ and $\text{Bin}(20, 0.5)$ distributions, respectively. Further, let $U = \min\\{X, Y\\}$ and $V = \max\\{X, Y\\}$. Then which of the following statements is/are correct?

• A. $E(U + V) = 19$
• B. $E(|X - Y|) = E(V - U)$
• C. $\text{Var}(U + V) = 16$
• D. $38 - (X + Y)$ has $\text{Bin}(38, 0.5)$ distribution

Answer 1

Answer: (A), (B), (D)

$E(U + V) = 19$

Answer 2

The correct option is (A): $E(U + V) = 19$,(B): $E(|X - Y|) = E(V - U)$ ,(D): $38 - (X + Y)$ has $\text{Bin}(38, 0.5)$ distribution