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Consider a quiz game show where you are given two questions to answer. Q1 will be answered correctlywith probability 0.8 and Q2 with probability 0.5. Answering Q1 correctly carries a reward of $ 1000 whileanswering Q2 correctly carries a reward of $ 2000. You get to choose the order in which you answer thequestions. The catch is that if you answer your first question incorrectly then the quiz terminates; you donot get a chance to attempt the second question. For a given order of answering the questions, let X bethe random variable that is the number of correctly answered questions and let g(x) be the total rewardreceived.(a) Suppose you answer Q1 first and then Q2. Find the expected reward, that is, E(g(X)).(b) Suppose you answer Q2 first and then Q1. Find E(g(X)).(c) In what order should you answer the questions to maximize your prize money?
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