I need help with the part b of the following question:
Let X have probability density function (pdf) given by
f(x) = ((12*x^2)+(4*x)) for 0 < x < (1/2)
a) Find the cdf of X.
b) Conditional on X = x, let Y be uniformly distributed on the interval (0, x).
Find the marginal pdf of Y , and use it to find E(Y ).