Please help using Bayesian Statistics way to solve this qeuestion, and give more details to solve c), d), e) questions. Thank you so much.

2 Galenshore distribution: An unknown quantity Y has a Galenshore(a, 0) distribution if its density is given by p(y) = 2 F(a) 02a2a-1-022 for y> 0,00 and a > 0. Assume for now that a is known. For this density, E[Y] F(a+1/2), E[Y] = (a) a 02 a) Identify a class of conjugate prior densities for 0. Plot a few members of this class of densities. b) Let Y., Y i.i.d. Galenshore(a, 0). Find the posterior distribution of given Y,, Yn, using a prior from your conjugate class. c) Write down p(0a|Y,..., Yn)/p(0|Y,..., Y) and simplify. Identify a sufficient statistic. d) Determine E[|y1,..., Yn] e) Determine the form of the posterior predictive density p(1, Yn).