Suppose you have a die that has probability p of resulting in the outcome 6 when rolled, where p is a continuous random variable that is uniformly distributed over [0, 1 suppose you start rolling this die. (the value of p does not change once you start rolling.) give exact answers as simplified fractions (a) compute the probability that the first roll is 6. (hint: the answer is not simply “p", since p is a random variable. think first about discrete uniform cases such as the one in which p can take 10/30, each with probability 1/10. from here, though, don't take the limiting case as the number of discrete values increases. instead, use the continuous analog of your discrete case and integrate.) compare your answer with the probability that the any of the 10 values 1/30, 2/ first roll is 6 if it were a fair die. (b) compute the probability that the first two rolls are both 6. (hint: you cannot assume without proof that the outcomes of two rolls are independent.) (c) let si be the event that the first roll is 6 and s2 be the event that the second roll is 6. compute (d) are the outcomes of the first two rolls independent? justify your answer. e) compute the probability that the first k rolls are each 6. compare this with the probability if it were a fair die.