Homework 7 - EE 351K PROBABILITY & RANDOM PROCESSES...

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Unformatted text preview: EE 351K PROBABILITY & RANDOM PROCESSES FALL 2011 Instructor: Sujay Sanghavi sanghavi@mail.utexas.edu Homework 7 Due: October 27th in class Focus: Limit Theorems, MAP Rule (Section 5.1-5.4, 8.1-8.2 in Textbook) Problem 1 Let X 1 , X 2 , ...be independent random variables that are uniformly distributed over [- 1 . 1] . For each of the following cases, find whether Y 1 , Y 2 , ...convergence to some limit in probability. (a) Y n = X n /n . (b) Y n = ( X n ) n . (c) Y n = min { X 1 ,...,X n } . (d) Y n = max { X 1 ,...,X n } . Problem 2 Suppose that X 1 , X 2 , ...are independent random variables, each with the exponential distribution with parameter = 1 . For n 2 , let Z n = max { X 1 ,...,X n } ln n . (a) Find a simple expression for the CDF of Z n . (b) Find the limit of this CDF. Is this limit a well-defined CDF? If not, regardless of all non-continuous points, what should the limit CDF be?...
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This note was uploaded on 02/20/2012 for the course EE 351k taught by Professor Bard during the Spring '07 term at University of Texas at Austin.

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Homework 7 - EE 351K PROBABILITY & RANDOM PROCESSES...

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