2. Let X be a single observation from Beta(0, 1) whose density function is, for a E (0, 1) and 0 > 0 f(x| 0) = 020-1 (a). Let Y = -(In X)-1. Compute the probability that the confidence coefficient 0 is in the set [y /2, y]. (b). Find a pivotal quantity and use it to set up a confidence interval having the same confidence coefficient as the interval in part (a). (c). Compare the two confidence intervals