Question

Let $(X_1, Y_1), (X_2, Y_2), \ldots, (X_{20}, Y_{20})$ be a random sample from the $N_2(0, 0, 1, 1, \frac{3}{4})$ distribution. Define
$\bar{X} = \frac{1}{20} \sum_{i=1}^{20} X_i \quad \text{and} \quad \bar{Y} = \frac{1}{20} \sum_{i=1}^{20} Y_i.$
Then $\text{Var}(\bar{X} - \bar{Y})$ is equal to:

• A. $\frac{1}{16}$
• B. $\frac{1}{40}$
• C. $\frac{1}{10}$
• D. $\frac{3}{40}$

Answer 1

Answer: (B)

$\frac{1}{40}$

Answer 2

The correct option is (B): $\frac{1}{40}$