ee302hw6_Fa11 - ECE302 Homework #6 Assigned 11/6/11, Due...

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Hint Hint: ECE302 Homework #6 ± 6 ± 6 6 →∞ →± () = += + =0 =0) == 0 = = + + X,Y XY V aX bY W cX dY. ad bc VW . ad bc a,b,c,d . W ± ±. Y<± Y>± ±± . . Assigned 11/6/11, Due 11/16/11 (by 4:30 in dropbox in MSEE 330) 1. Text. chapter 5, problem 5.95. 2. Text, chapter 5, problem 5.96 3. Text, chapter 5, problem 5.106. 4. Text, chapter 5, problem 5.113. (a) : switch to polar coordinates to evaluate integrels (b) the conditioning event is determined by . 5. Let and be independent zero-mean unit variance Gaussian random variables. Let and (a) Assume i. Show that independent Gaussian random variables are jointly Gaussian. ii. Find the mean, variance and correlation coefficient of and iii. Find the joint pdf of and iv. Find the conditional mean and variance of given v. Find the conditional pdf of given (b) Assume (and for convenience In this case it can be shown that where (you don±t need to show this). i. Are and jointly continuous? ii. Find iii. Find the correlation coefficient as a function of iv. Find the conditional pdf of given (you cannot get this from part (a)). v. Find the joint pdf of and (you cannot get this from part (a)).
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This note was uploaded on 02/14/2012 for the course ECE 302 taught by Professor Gelfand during the Spring '08 term at Purdue University-West Lafayette.

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ee302hw6_Fa11 - ECE302 Homework #6 Assigned 11/6/11, Due...

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