A03.2 BetaGamma Let X ~ Beta(a, B) and Y ~ Gam(o, B) with pdfs respectively [(atB) fx (2 ) = Tar(B-(1 -x)3-1 y E (0, 1) O otherwise and fr(y) = Toyo-le-By y>0 0 otherwise for o > 0 and 3 > 0. Use the unit-integrability property to show that E [X] = a/(a + 3) and to find E Ye-2Y]. [7]