7-1. If X has the Gam(o, A) distribution, we calculated in class that E(XB) _ I(a + B) T(Q)AB (a) Find E(X?) (b) Find var(X). None of your answers should contain gamma functions (use the gamma function recursion formula to simplify). 7-2. If X has the Beta(o1, 02) distribution, show that _[(a1 + 02)(a1 + BI)I(@2 + 32) EXB(1 -X) ) =To) )I (@2) [ (a + 02 + Bit B2) Hint: use the fact that the PDF of the beta distribution integrates to one, just like we did for the gamma distribution. You may ignore the issue of when the integral exists (it exists when B1 > -01 and B2 > -02, but we don't know how to prove that yet). 7-3. Suppose X has the Beta(01, 02) distribution. (a) Find E(X). (b) Find E(X2). (c) Find var(X). None of your answers should contain gamma functions (use the gamma function recursion formula to simplify). Hint: use the result of problem 7-2