Consider a game where a fair coin is flipped if the coin, Operation Management

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Consider a game where a fair coin is flipped if the coin

Consider a game where a fair coin is flipped. If the coin comes up heads, you win your bet; if it comes up tails, you lose your bet. At each new flip, however, you must double your bet from the previous flip. You begin with $31 in your bank account. Your initial bet is $1. The game continues until you see a head or when you go negative for the first time.

(a) What is the set of outcomes of this experiment? What is the probability of each outcome?

(b) Let X be the random variable which represents the gain or loss from each outcome. What is the expectation of X?

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Operation Management: Consider a game where a fair coin is flipped if the coin

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