4. In a series of games, the wining number of the nth game, n=1,2,3,.. is a...

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4. In a series of games, the wining number of the nth game, n=1,2,3,.. is a number selected at random from the set of integers {1,2, .., n+ 2}. John bets n dollars in game n and says he will quit a soon as he wins. Also, if he wins game number n, then he is paid n? dollars. a. Find the probability that he has to play indefinitely. Note: Use only the concept of increasing/decreasing sequence of events in your solution and define the events clearly. b. Let Y be the number of games he has to play. Find P(Y =n). c. Let W denote his net amount of money when he quits playing. Find P(W > through the PMF of Y. Note: your solution should not be based on enumeration. 4. In a series of games, the wining number of the nth game, n=1,2,3,.. is a number selected at random from the set of integers {1,2, .., n+ 2}. John bets n dollars in game n and says he will quit a soon as he wins. Also, if he wins game number n, then he is paid n? dollars. a. Find the probability that he has to play indefinitely. Note: Use only the concept of increasing/decreasing sequence of events in your solution and define the events clearly. b. Let Y be the number of games he has to play. Find P(Y =n). c. Let W denote his net amount of money when he quits playing. Find P(W > through the PMF of Y. Note: your solution should not be based on enumeration.

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Answer Explanation a The probability that the game is played inde... View the full answer