McGill University, Faculty of Engineering Course ECSE-305A: Probability and Random Signals I Midterm Examination #2, Fall 2004 Date and time: Wednesday, November 10, 2004, 10:35 - 11:25 Examiner: Prof. B. Champagne and Prof. Y. Psaromiligkos Instructions: This is a closed book examination: only the faculty standard calculator is allowed. Attempt all questions. 1. Let X be an RV with the following pdf 20 marks f ( x ) = αδ ( x ) + βx 2 , x ∈ (-1 , 1) , for some α,β >0 . (a) Find a relationship between α and β . (b) For n a positive integer, ﬁnd E ( X n ), the n th moment of X . (c) Find α and β such that Var( X ) = 1 / 5. 2. Let X be a uniform RV on the interval (
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