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**Janu42** 1) Use the fact that $\displaystyle {(n-1)S^2\over \sigma^2}$ is a chi square random variable with n-1 degrees of freedom to prove that

$\displaystyle Var(S^2)$=$\displaystyle 2\sigma^4/n-1$.

*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