2. Independent random variables U and V each take the values −1 or 1 only, and P(U = 1) =

a, P(V = 1) = b, where 0 <

a, b < 1. A third random variable W is defined by W = UV. Show that there are unique values of a and b such that U, V , and W are pairwise independent. For these values of a and

b, are U, V , and W independent? Justify your answer. (Oxford 1971F)