Let $X _ { 1 } , \ldots \ldots , X _ { 8 }$

Short Answer

Let $X _ { 1 } , \ldots \ldots , X _ { 8 }$ be a random sample from a normal distribution with variance $\sigma _ { 1 } ^ { 2 } \text {, and let } Y _ { 1 } , \ldots \ldots , Y _ { 10 }$ be another random sample (independent of the $\left. X _ { 2 } ^ { \prime } s \right)$ from a normal distribution with variance $\sigma _ { 1 } ^ { 2 } \text {, and let } S _ { 1 } ^ { 2 } \text { and } S _ { 2 } ^ { 2 }$ denote the two sample variances. Then the random variable $F = \left( S _ { 1 } ^ { 2 } / \sigma _ { 1 } ^ { 2 } \right) \left( S _ { 1 } ^ { 2 } / \sigma _ { 1 } ^ { 2 } \right)$ has an F distribution with $v _ { 1 } =$$\underline{\quad\quad}$ and $v _ { 2 } =$$\underline{\quad\quad}$