Let X and Y have a joint density

f(x, y) =

{24x * (1 - y), 0

{0 otherwise

a) Find value of P(Y > 2X).

b) Find marginal distribution of Y . Identify it as a famous distribution and its parameters.

c) Explain how the joint density f arises from independent random variables each of which has the uniform distribution on the interval (0, 1).