Let X and Y be independent (strictly positive) gamma random variables with parameters (r1, ) and (r2, ), respectively. Define U = X + Y and V = X/(X + Y ). (a) Find the joint probability density function of U and V . (b) Prove that U and V are independent. (c) Show that U is gamma and V is beta.

Elementary Statistics Notes Amanda Selly 8/29/2016 Mean: average To find the mean you add up all the values and then divide by the number of values you have o Population mean: µ= x1+x2+x3+…+xN/N µ= Σx/N o Sample mean: ~x= x1+x2+x3+…+xn/n µ= Σx/n Please note that sample mean is indicated by an x with a bar on...