NEED ANSWER FOR PART b,c and d only.

PLEASE SHOW THE WORKING OF THE PARTS!! THANK YOU :))

Question 8: Answer each of the following: (a) A single multiple choice question on a test has n choices, only one of which is correct. A student who does not know the answer will guess randomly, while a student who does know the answer will answer correctly. The probability that a student taking this test knows the answer is p. Find the conditional probability that the student knew the answer, given that the question was answered correctly. (b) Let X| have a Poisson distribution with parameter 1 > 0. Suppose that itself is random, following an exponential distribution with parameter 0. What is the conditional distribution of 1|X = x? - (c) Let continuous random variable X have a uniform distribution over the range (-1, 1) and let Y = X2. Prove that X and Y are uncorrelated. Does this imply that they are independent random variables? (d) Explain and discuss the Bayesian method of estimation of the parameters of a statistical model. Question 8: Answer each of the following: (a) A single multiple choice question on a test has n choices, only one of which is correct. A student who does not know the answer will guess randomly, while a student who does know the answer will answer correctly. The probability that a student taking this test knows the answer is p. Find the conditional probability that the student knew the answer, given that the question was answered correctly. (b) Let X| have a Poisson distribution with parameter 1 > 0. Suppose that itself is random, following an exponential distribution with parameter 0. What is the conditional distribution of 1|X = x? - (c) Let continuous random variable X have a uniform distribution over the range (-1, 1) and let Y = X2. Prove that X and Y are uncorrelated. Does this imply that they are independent random variables? (d) Explain and discuss the Bayesian method of estimation of the parameters of a statistical model