a)

Since ,

and then

Now you have to look for a standarized normal table and look

for which the value of z such that P(Z < z) = 1/3.

b) Here you just have to find the distribution of W = X - Y. It can be done

using the Jacobian method, for example.

c) From letter b) you know what is the distribution of W, so

its expectation value and variance are also known. The formula to

compute the expectation and variance of a uniform variable are easily

obtained and then you have two equations with two unkown variables a and b.

Solve the system.