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Starting on day n = 1, you buy one lottery ticket each day. Each ticket costs 1 dollar and is independently a winner than

 

Starting on day n = 1, you buy one lottery ticket each day. Each ticket costs 1 dollar and is independently a winner than can be cashed for 5 dollars with probability 0.1; otherwise the ticket is worthless. Let Xn equal your net profit after n days. What is E[Xn]?

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