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David is writing an exam consisting of 30 questions. For each question, the prob

ID: 3395761 • Letter: D

Question

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.

Explanation / Answer

David is writing an exam consisting of 30 questions. For each question, the prob

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