Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { n }$

Essay

Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { n }$ be a random sample from a normal distribution with mean $\mu$ and variance $\sigma ^ { 2 }$ . Then the random variable $( n - 1 ) S ^ { 2 } / \sigma ^ { 2 }$ has a __________ probability distribution with __________ degrees of freedom.