Question

Let $X_1, X_2, \ldots, X_{20}$ be a random sample from the $N(5, 2)$ distribution, and let $Y_i = X_{2i} - X_{2i-1}$ for $i = 1, 2, \ldots, 10$. Then $W = \frac{1}{4} \sum_{i=1}^{10} Y_i^2$ has the distribution:

• A. $t_{20}$ distribution
• B. $\chi^2_{20}$ distribution
• C. $\chi^2_{10}$ distribution
• D. $N(250, 20)$ distribution

Answer 1

Answer: (C)

$\chi^2_{10}$ distribution

Answer 2

The correct option is (C): $\chi^2_{10}$ distribution