1) Use the fact that / is a chi square random variable with n-1 degrees of freedom to prove that
= .
Hint: Use the fact that the variance of a chi square random variable with k degrees of freedom is 2k.
2) Let V and U be independent chi square random variables with 7 and 9 degrees of freedom, respectively. Is it more likely that (V/7)/(U/9) will be between
a) 2.51 and 3.29 or
b) 3.29 and 4.20