b) d) If at rst you don't succeed Suppose that you believe that students will each succeed on a given test of skill with probability S, and that success on each trial is conditionally independent given 5. Suppose that you believed S was equally likely to be 1! 3 or 1.2 before you observed six successes and six failures. Now what do you believe? Suppose that you believe 3 is equally likely to be 1." 3 or \"2, and consider the number of successes in the next twelve trials. Find its expected value and variance. Suppose that you believe that S w Beta (10, 15). Consider the number of successes in the next twelve trials. Find its expected value. If you observed six successes in those trials, what would you then believe about 5? Suppose that you believe that S ~Uni1"orrn([}, 1). Consider the number of successes in the next twelve trials. Find its expected value. If you observed six successes in those trials, what would you then believe about 3