Problem 4 Let X ~Uniform[0, 1], and Y = vX. Find E(Y), E(Y?) and Var(Y) by (a) finding the density of Y and then finding the expectation and (b) using the formula on P10 of the slides.13. If X is a nonnegative continuous random variable, show that E(X) = [1 - F(x)]dx 0 Apply this result to find the mean of the exponential distribution.