4. Consider a random sample \( \{x{1},\ldots ,x{n}\} \) from the distribution with mean \( \mu \) and known variance \( \sigma^2 \) . Define

$$\bar{x} = n^{-1} \sum{i=1}^{i=n} xi, si^2 = (n-2)^{-1} \sum{i=1}^{i=n} (xi - \mu)^2, \text{ and } s2^2 = (n-2)^{-1} \sum{i=1}^{i=n} (xi - \bar{x})^2. \text{ If } n=60, \text{ the distributions of } (n-2)s1^2/\sigma^2 \text{ and } (n-2)s2^2/\sigma^2 \text{ are __, respectively. (10%) (Justify your answers)}$$