6. (7 pts) For a uniform distribution with density function (b - a) if rela, b) f(x) = 0 otherwise prove that the formulae for calculating the mean and variance are given by: E(X) = (a + b) V(X) = 1(b -a)2 The following identities may be useful: 62 - a2 = (b - a)(b + a) and (b - a)3 = 63 - 3ab- + 3a2b -a3. Similarly, this identity might be used as well: 63 - a3 = (b -a) (b2 + a2 + ab)