On the F distribution: (a) Derive the variance of the F distribution. (b) If X has an F distribution with m and n degrees of freedom, argue that 1/X has an F distribution with n and m degrees of freedom. (c) If X has an F distribution with m and n degrees of freedom, show that has a beta distribution. W mx/n +mX/n (d) Use the result of part (c) and the beta function to find the mean and variance of the F distribution. [Find the first two moments of mX/n= W/(1-W)].