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# problemset13 - STAT/MA 416 Problem Set 13 Name 1 Winnings...

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STAT/MA 416 September 21, 2011 Problem Set 13 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. (a.) What is his expected gain or loss? (b.) What is the variance of his gain or loss? (c.) Find constants a, b such that if X = 0 when he loses and X = 1 when he wins, then Y = aX + b is his earnings. [Hint: solve 5 = a (1) + b and - 4 = a (0) + b . Also: X is a Bernoulli.] Verify your results above by finding E ( Y ) and Var( Y ) with this method. 1

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2. Telemarketers. One out of every eight calls to your house is a telemarketer. You will record whether the next call is a telemarketer. (a.) What is the probability that the next time the phone rings, it will be a telemarketer? (b.) If the phone calls are independent, what is the probability the 3rd call after dinner will be a telemarketer? (c.) If you lose 30 seconds of your time every time you have to talk to a telemarketer, what is the expected amount of time you will lose on the next phone call?
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