Let X be a random variable with a Student's t distribution with p degrees of freedom.
(a) Derive the mean and variance of X.
(b) Show that X2 has an F distribution with 1 and p degrees of freedom.
(c) Let f(xp) denote the pdf of X. Show that

at each value of xi -oo oo, X converges in distribution to a n(0,1) random variable. (Hint: Use Stirling's Formula.)
(d) Use the results of parts (a) and (b) to argue that, as p †’ oo,X2 converges in distribution to a X2i random variable.
(e) What might you conjecture about the distributional limit, as p †’ oo, of q Fq,p?

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