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Unformatted text preview: heads the ﬁrst time, 2 rubles if it shows the ﬁrst head at second toss, and in general 2 k-1 if the dealer tosses the coin k times to get the ﬁrst head. 1. Suppose the ﬁxed wager is 10 rubles. What is the expected amount of money that the gambler will win in this game? Suppose the ﬁxed wager is 10,000 rubles? 2. What is the probability that the gambler does not lose money in a game when the ﬁxed wager is 10 , 000 rubles ? 3. In reality, it would not be reasonable for the gambler to play the game with the ﬁxed wager at 10 , 000 rubles. Why? (Hint: Suppose the casino has a limit of a billion rubles.) Problem 5 If the random variable X takes values in non-negative integers, prove that: E [ X ] = ∞ X t =0 Pr( X > t )...
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- Fall '07
- Probability theory, St. Petersburg, St. Petersburg Casino, fixed wager