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Please see the problem in the attachment. 4. Concentration Bounds [5 points, 5 points, 5 points] A gambler bets one dollar in each game. She

Please see the problem in the attachment.

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4. Concentration Bounds [5 points, 5 points, 5 points] A gambler bets one dollar in each game. She wins two dollars with probability 0.3, one dollar with probability 0.2 and zero dollar with probability 0.5. Please use Chebyshev's inequality, the central limit theorem and the Cherno bound to estimate the probability that she is ahead after 400 games

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