4. Suppose there are N multiple-choice questions in an examination. Each question has 4 choices. You have a probability of 0.6 of knowing the correct answer to a particular question. If you do not know the answer, you pick one at random. Your answer to different questions are independent of each other. (a) For a particular question, find the probability that you answer it correctly. [3 marks] (b) Suppose N = 3. Given that you have answered all questions correctly, what is the probability that you only know the answer to exactly two questions? [5 marks] (c) The time T to answer a particular question has the following density function: fr(t) = I exp(-)t), if you know the answer; 41 exp(-4Xt), otherwise. i. Find E(T). You can use the mean of an exponential distribution without proof, but you need to state it clearly. [5 marks] ii. Let T; be the time to answer the ith question. The T's are independent of each other and identically distributed to T. Let W be the total time to answer all questions. Find E(W) and Var(W) if you are given that Var(T) = 19/(25/), E(N) = Var(N) = 20. =