  # Two questions are presented to a contestant on a show. The contestant is to attempt both questions and can startwith either question 1 or 2. No matter which question he starts with, he must answer the question correctly beforethe other question can be attempted. Suppose the probability is qi that he correctly answers question i (that is qfor correctly answering question 1 and q2 for correctly answering question 2. Furthermore, for a correct answer,the contestant receives W dollars (that Wi for correctly answering question 1 and W2 for correctly answeringquestion 2). Assume that knowing the answer to one question is independent of knowing the answer to the secondquestion. What is the pmf of X, the contestants winnings, if he started with question 1? What is the pmf of Xthe contestants winnings, if he started with question 2?

Question

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Step 1

It is given that the probabilities of answering 1st and 2nd questions are q1 and q2 respectively. And the amount will receive for correctly answering 1st and 2nd questions are W1 and W2 respectively. Also it is given that knowing the answer to one question is independent of knowing the answer to another.

Step 2

The probability mass function (PMF) for the winnings of the cont...

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