Question: Suppose I play a gambling game where I either win or lose k dollars. Suppose further that the chance of winning is p5. I

Suppose I play a gambling game where I either win or lose

Suppose I play a gambling game where I either win or lose k dollars. Suppose further that the chance of winning is p5. I employ the following strategy to try to guarantee that I win some money. I bet RM1; if I lose, I double my bet to RM2, if I lose I double my bet again. I continue until I win. Eventually I'm sure to win a bet and net RM1 (run through the first few rounds and you'll see why this is the net). If this really worked casinos would be out of business. Our goal in this problem is to understand the flaw in the strategy. fa) Let X be the amount of money bet on the last game (the one I win). X takes values 1, 2, 4, 8,.... Determine the probability mass function for X. That is, find p(2k), where k is in {0, 1, 2, ...). 6.5 1+ (b) Compute E(X). (c) Use your answer in part (b) to explain why the strategy is a bad one.

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