Suppose that X is a uniform random variable on [0,2] and Y is a uniform random variable on [1,2]. Assume further that X and Y are independent.

Suppose that X is a uniform random variable on [0,2] and Y is a uniform random variable on [1,2]. Assume further that X and Y are independent. Find

a) The joint probability density of X and Y;

b) The density function of Z = X + Y;

c) P{X + Y =< 2}.

Thank you in advance!