1. Give an example of a sample space together with a probability rule P and four independent (non-trivial) random variables X, Y, Z and T which are all defined on . (A random variable X : R is non-trivial if it gets at least two different values with non-zero probability.)

2. With the example in part (1), show that U = XY and V = Z + T are independent. (Show by formulae, not by explanation.)