Question: Michael is trying to budget time for his problem set. He knows that the number of problems on the problem set is Poisson(6) distributed, and

Michael is trying to budget time for his problem set. He knows that the number of problems on the problem set is Poisson(6) distributed, and the probability that he can solve any given problem is -, and is independent of all other problems. If he can solve the problem, the amount of time he spends on the problem is Exponential (-) distributed; otherwise, the amount of time he spends on the problem is Exponential (-) distributed. What is the expected amount of time that Michael will spend on the problem set

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