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Unformatted text preview: McGILL UNIVERSITY FINAL EXAMINATION Faculty of Engineering Fall 2005 ECSE 305, Section 001 (CRN 583) PROBABILITY AND RANDOM SIGNALS I DATE: Thursday, December 8, 2005 TIME: 9:00 – 12:00 Examiner: Prof. Benoˆ ıt Champagne Associate Examiner: Prof. Yannis Psaromiligkos Signature: Signature: INSTRUCTIONS: • This is a CLOSED BOOK examination. • Faculty standard calculator permitted ONLY. • This examination paper consists of 5 printed pages, including: a cover page, 6 questions and an appendix. Ensure that you have a complete examination before starting. • Answer ALL questions. Use one or more Answer Booklets for your solutions. • You MUST RETURN this examination paper. December 8, 2005 (9:00 – 12:00) 1/5 1. A bank has two cashiers A and B. The time it takes cashier A to serve a customer 20 marks is exponentially distributed with parameter λ A = 1 8 minutes- 1 , while the time it takes cashier B to serve a customer is again exponentially distributed but with parameter λ B = 1 5 minutes- 1 . Since cashier A is closer to the bank’s entrance it has been observed that 70% of the bank’s customers go to him. (a) Let X denote the service time of a randomly selected customer. Find the cumulative distribution function (CDF) of X . (b) Find the probability density function (PDF) of X . (c) What is the mean of X ? (d) A customer just came out of the bank and tells you that in his case the service time was less than 6 minutes. What is the probability that he was served by cashier A? (e) If the same customer had asked you to guess if he was served by cashier A or B, what would be your guess? Justify your answer....
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