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# mid06number2 - McGill University, Faculty of Engineering...

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McGill University, Faculty of Engineering Course ECSE-305A: Probability and Random Signals I Midterm Examination #1, Fall 2006 Date and time: Friday, November 10, 2006, 10:35 - 11:25 Examiner: Profs. B. Champagne and Y. Psaromiligkos Instructions: This is a closed book examination: only the faculty standard calculator is allowed, NO crib sheet. Attempt all questions. NOTE: This exam spans 2 pages 1. The CDF of random variable X is given by 20 marks F ( x ) = a, x < - 1 bx + c, - 1 < x < 0 bx + d, 0 < x < 1 e, x > 1 where a,b,c,d and e are unspeciﬁed constants. It is also known that P ( | X | = 1) = 0 and P ( X = 0) = 1 / 3. (a) Find the constant values a,b,c,d and e and sketch the graph of F ( x ). (b) Show that X is a mixed RV. That is, identify the 4 components entering the deﬁnition of a mixed RV as seen in class. (c) Find the PDF of X and sketch its graph. 2. Assume that the temperature T measured in o C (degrees Celsius) at noon time in 20 marks Montreal during the month of April is a normal (Gaussian) random variable. Further, it is

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## This note was uploaded on 09/30/2009 for the course ECSE 305 taught by Professor Champagne during the Spring '09 term at McGill.

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mid06number2 - McGill University, Faculty of Engineering...

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