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Unformatted text preview: Quiz #5 Friday, October 5 th NAME: ______________________________ Grade: __________ out of 25. You have 30 minutes to complete this Quiz. This Quiz is a closed book and Notes exam Exercise 2 is on the other side of the test. Exercise 1: (10 points) Lets say that there are only 5 airline companies in U.S. which are companies A, B, C, D, E. Let our random variable: X = airline preferred by a Frequent Flyer The probability mass function of X is as follows: Airline x A B C D E P(X=x) 0.1 c c-0.2 0.3 0.1 a) (5 points) Find the value of c? b) (5 points) Draw a graph of the pmf a) 0.1 +c + c-0.2 +0.3 +0.1 = 1 => 2c=0.7 => c=0.35 b) A B C D E Airlines p(x) 0.10 0.20 0.30 Exercise 2: (20 points) The Department of Statistics has 10 graduate student positions every year. Because many students reject the position and they do not want to risk having less than 10 new students, they usually accept 15 students, hoping that at least 10 of them will accept the position. The cumulative distribution function of random variable X= the people who finally accept the offer is the following: ( 29 0, 7 0.02,7 8 0.02,8 9 0.23,9 10 0.47,10 11 0.77,11 12 0.87,12 13 0.95,13 14 1, 14 x x x x F x x x x x x < < < < = < < < < a) (5 points) Find the probability mass function of X b) (5 points) Draw the graph of cumulative distribution function of X c) (5 points) Find ( 29 10 P X o and ( 29 9 11 P X o using only the cumulative distribution function d) (5 points) If student A is the first on the waiting list, that is he is the 16 th person on Departments list and he will get an acceptance letter only if less than 10 people of the first 15 accept the position. What is the probability student A will NOT receive an acceptance letter?acceptance letter?...
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- Fall '08