Problem 4. For p > 0 and q > 0, let B(p, q ) := up-1(1 - u)4-'du 0 called the Beta function. Consider 2P-1 f ( 2 ) := B(p, q) (1 + z ) ptq: 2> 0. Show that f(z) is a valid density. Hint: Make the change of variable t = 1/(1 + z)