Forget question a. I do not how to solve question b and c. Please help me with these, I need thorough explanations and references to general equations. Thanks

8. Random variables X and Y have joint density _. c(y\"w2)e'y y5z5y, y>0 fx,y(.'l:,y) _{ 0 otherwise Here 6 is a constant. a) Show that Y has a gamma density, and hence deduce that c = 1/8. b) Find the density of 4Y3. c) Explain why E( IX I) is at most 4