Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Tutorial 6 October 21/22, 2010 1. Let X be a discrete random variable with PMF pX and let Y be a continuous r andom variable, independent from X, with PDF fY . Derive a formula for the PDF of the random variable X +Y . 2. The random variables X and Y are described by a joint PDF which is constant within the unit area quadrilateral with vertices (0, 0), (0, 1), (1, 2), and (1, 1). Use the law of total variance to find the variance of X + Y . 3. (a) You roll a f air six-sided die, and then you flip a fair coin the number of times shown by the die. Find the expected value and the variance of the number of heads obtained. (b) Repeat part (a) for the case where you roll two dice, instead of one. Page 1 of 1MIT OpenCourseWare http://ocw.mit.edu 6.041 / 6.431 Probabilistic Systems Analysis and Applied Probability Fall 2010 For information about citing these materials or our Terms of Use, visit:
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