David is writing an exam consisting of 30 questions For each

David is writing an exam consisting of 30 questions. For each question, the probability that David is not sure how to do it is 0.1.

(a) It takes David 5 minutes to solve a question that he is sure and 20 minutes for a question that he is not sure. Let X be the total time that David finishes the exam. Find the expected value and variance of X.

(b) Let Y be the number of questions that David is not sure. If it takes David 5 minutes to solve a question that he is sure and (4Y 2 + 16) minutes to finish all those questions that he is not sure. Let X be the total time that David finishes the exam. Find the expected value and variance of X.

Solution