2. Suppose a random variable U ~ unif(0, 1). () Compute the mean and variance of U. (You need to show the details of your work.) (by Compute the mean and variance of - In U. (c) Next, consider another set of independent random variables Y1, . ..; Ym, where each Y: is related to U; through Y; = -0In Uj, where U; ~ unif(0, 1) and 0 > 0. i. Compute E(Y,). Can you suggest a reasonable estimator for e? ik Write down the log-likelihood function from the random variables Y1, . .., Yr