If Xis uniformly distributed on [a, b], show that Y = (X - a)/(b - a) is uniformly distributed on [O, l]. Using the fact that X = a + (b - a)Y and the expectation and variance of a uniformly...

If Xis uniformly distributed on [a, b], show that Y =

(X - a)/(b - a) is uniformly distributed on [O, l]. Using the

fact that X = a + (b - a)Y and the expectation and variance of

a uniformly distributed variable on [O, l], show that E(X) =

(a + b)/2 and Var(X) = (b - a) 2/12.