AK8_230 - ECO 230 Economic Statistics Answer Key to...

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ECO 230 Marianna Kudlyak Economic Statistics Spring 2007 Answer Key to Homework #8 Total points: 10. Exercise 1 . Newbold, Carlson and Thorne, Problem 6.75, p.227. Exercise 2 . Newbold, Carlson and Thorne, Problem 6.91, p.228. Exercise 3. The amount of time before the first score by either team in college hockey games is exponentially distributed with a mean of 8.7 minutes. Consider a sample of 100 games a team played over the last years. Assuming that the games are independent, what is the probability that in more than 20% of the games, the first period ends with neither team scoring? A period in hockey lasts 20 minutes. Probability that the first period ends without a goal: P(T>20), where T is an exponentially distributed random variable that denotes time between the start of the first period and the first goal. Hence, λ 20 20 ) 1 ( 1 ) 20 ( 1 ) 20 ( = = < = > e e T P T P For exponential distribution we have 10 . 0 ) 20 ( 7 . 8 1 7 . 8 1 ) ( 7 . 8 20 = = > = = = e T P T E
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Let X be random variable that denotes number of games in the sample of 100 in which the first period ends with no goal. The exact distribution of X is binomial with sample size n = 100 and p = P(T>20) = 0.1. We want to find P(X>20).
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This note was uploaded on 06/09/2008 for the course ECO 230 taught by Professor Kudlyak during the Spring '08 term at Rochester.

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AK8_230 - ECO 230 Economic Statistics Answer Key to...

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