STAT230_Final_Summer08 - American University of Beirut STAT...

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Unformatted text preview: American University of Beirut STAT 230 Introduction to Prob0ability and Random Variables Summer 2008 Final Exam Name: ............................... ID #: ................................. Section: 4 (7:30) 6 (12:30) Exercise 1 (10 points) The number of accidents in a period of one week follows a Poisson distribution with mean two. The number of accidents from week to week are independent. Find the probability of exactly seven accidents in a given three weeks. Exercise 2 Let X be a continuous random variable with pdf f ( x ) = kx 2 e- x 2 / 2 , < x < + ∞ a. (10 points) find the value of the constant k b. (10 points) find E ( X ) and V ar ( X ) Exercise 3 (20 points) Let X 1 and X 2 be independent χ 2 (2) distributions, i.e. f ( x ) = 1 2 e- x/ 2 < x < + ∞ find the joint pdf of Y 1 = X 1 + X 2 and Y 2 = X 1- X 2 , then find the marginal pdf of Y 2 Exercise 4 (20 points) Flip n = 8 fair coins and remove all that come up heads. Flip the other (tails) coins and remove the heads. Continue flipping the remaining coins until each has come(tails) coins and remove the heads....
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This note was uploaded on 03/01/2010 for the course STAT 230 taught by Professor Variousteachers during the Spring '10 term at American University of Beirut.

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