problemset15

# problemset15 - STAT/MA 416 Problem Set 15 Name 1 Winnings...

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STAT/MA 416 September 26, 2011 Problem Set 15 Name: 1. Winnings and Losing. Suppose that a person wins a game of chance with probability 0 . 40, and loses otherwise. If he wins, he earns 5 dollars, and if he loses, then he loses 4 dollars. He plays the game until he wins for the first time, and then he stops. Assume that the games are independent of each other. Let X denote the number of games that he must play until (and including) his first win. (a.) How many games does he expect to play until (and including) his first win? (b.) What is the variance of the number of games he plays until (and including) his first win? (c.) What is the probability that he plays 4 or more games altogether? 1

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2. Winnings and Losing (continued). Continue to use the scenario from the previ- ous problem. As before, let X denote the number of games that he must play until (and including) his first win. (a.) Find a formula for his gain or loss, in terms of X . I.e., if Y denotes his gain or loss in dollars, write Y in terms of X .
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