1.4.(10%) Consider a random sample $X_i, i=1, \dots, n$. Let $\mu$ and $\sigma^2$ denote the

population mean and variance. Define $\bar{X} = n^{-1} \sum{i=1}^n Xi$, $s1^2 = n^{-1} \sum{i=1}^n (Xi - \mu)^2$, $s2^2 = n^{-1} \sum{i=1}^n (Xi - \bar{X})^2$, What are the distributions of $ns1^2/\sigma^2$ and $ns2^2/\sigma^2$ if n=50? (Justify your answers)