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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?
(c) Would you agree to play this game? If you had more money, would you play this game?
Could someone please help me with this problem?
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