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EE351KHW_8Fall2007

# EE351KHW_8Fall2007 - 2 XY E −(c 6 4 Y X V − −(d If Y...

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THE UNIVERSITY OF TEXAS AT AUSTIN Department of Electrical and Computer Engineering EE351K, Probability and Random Process, Fall 2007 Assignment No. 8; Due Thursday, October 25, 2007 1. For the following joint pmf, find the following. X Y 1 2 -2 3/8 1/8 3 2/8 2/8 (a) Marginal pmf’s, ) ( x p X and ) ( y p Y (b) Expected values, ] [ X E and ] [ Y E (c) Variances, ] [ X V and ] [ Y V (d) Conditional pmf’s, ) | ( | y x p Y X and ) | ( | x y p X Y (e) Conditional expectations, ] | [ y Y X E = and ] | [ x X Y E = (f) Are X and Y independent? (g) ) 3 , 5 . 1 ( Y X P (h) ) 3 | 0 ( = Y X P (i) Calculate ] [ X E from ] | [ y Y X E = . (j) Calculate ] [ Y E from ] | [ x X Y E = . (k) Calculate ] , [ Y X Cov and Y X , ρ .

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