Here is my Problem.

Let X~Uniform(0,2) and Y~Normal(0,1) be independent random variables. Let

Z ={1 if X > Y

{2 if X <Y

Find E[Z] and V ar[Z]. You may leave your answers in terms of denite integrals.

My big question is, how can we join a uniform and a normal distribution on the same probability density function.

Thank you