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ENGR 371 - Final Exam Summer 2003

# ENGR 371 - Final Exam Summer 2003 - 1 Concordia University...

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1 Concordia University Department of Electrical and Computer Engineering ENGR 371 - Probability and Statistics Instructor: Dr. A. Ghrayeb Final Exam Summer 2003 - 20/8/2003 ================================================================================= 1) (15 Marks) Give a precise, concise de f nition of the following: a) An event. b) A random variable. c) A population. d) A con f dence interval. e) Statistical inference. 2) (15 Marks) Let X 1 ,X 2 ,...,X n be independent, normally distributed n random variables with means µ 1 2 , ... , µ n and variances σ 2 1 2 2 ,,. ..,σ 2 n , respectively. Let Y be another random variable de f ned as Y = n P i =1 X i Find the probability distribution function of Y, g ( y ) , using the notion of moment-generating functions .( Show all work. ) You are given that the moment-generating function of a random variable X with mean µ and variance σ 2 is given by M X ( t )= e jµt σ 2 t 2 / 2 . 3) (15 Marks) Let X and Y be zero-mean, unit-variance independent normal random variables. Find the joint probability distribution function of V and W de f ned by V = p X 2 + Y 2 W = ( X,Y ) , where θ

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ENGR 371 - Final Exam Summer 2003 - 1 Concordia University...

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