Hw5 - λe-λx and λe-λy respectively Let Z = X Y Find the conditonal PDF of X given Z = z Problem 4 Let X and Y be two random variables that are

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EE 351K Probability, Statistics, and Random Processes SPRING 2009 Instructor: Shakkottai/Vishwanath { shakkott,sriram } @ece.utexas.edu Homework 5 (Due 03/09/2009) Problem 1 Consider two continuous random variables Y and Z and a random variable X that is equal to Y with probability p and to Z with prbability 1 - p . Show that the PDF of X is given by f X ( x ) = pf Y ( x ) + (1 - p ) f Z ( x ) Problem 2 The random variable X has the PDF f X ( x ) = ± cx - 2 , 1 x 4 0 , otherwise 1. Determine the value of c . 2. Let A be the event { X > 2 } . Calculate P ( A ) and the conditional PDF of X given that event A has occured. Problem 3 Let X and Y be two identical, but independent exponential random variables with PDFs
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Unformatted text preview: λe-λx and λe-λy respectively. Let Z = X + Y . Find the conditonal PDF of X given Z = z . Problem 4 Let X and Y be two random variables that are independent and uniformly distributed over the interval [0 , 1] . Find the CDF and PDF of | X-Y | . Problem 5 Find c and the PDF of the continuous random variable X associated with the moment generating function M X ( s ) = c. 3 3-s + 3 4 . 7 7-s ....
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This note was uploaded on 10/26/2009 for the course EE 351k taught by Professor Bard during the Spring '07 term at University of Texas at Austin.

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