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Suppose I play a gambling game where I either win or lose k dollars. Suppose further that the chance of winning is p = .5. I employ the following strategy to try to guarantee that I win some money. I bet $1; if I lose, I double my bet to $2, if I lose I double my bet again. I continue until I win. Eventually I’m sure to win a bet and net $1 (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. (a) 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, . . . }. (b) Compute E(X). (c) Use your answer in part (b) to explain why the stategy is a bad one.
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Consider a big decision that you have made. Write a description of the decision using the steps in the decision-making process as your guide. What could you have done differently in the process to improve your decision? (Word limits up to 250)
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Who launched the protestant reformation in the 1500's? A) Henry VIII B) John Wycliffe C) John Calvin D) Martin Luther