EE351KHW_11Fall2007 - x y f X Y(e Are X and Y independent(f Find | y Y X E = and | x X Y E = and then X E and Y E from the conditional

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THE UNIVERSITY OF TEXAS AT AUSTIN Department of Electrical and Computer Engineering EE 351K • Probability and Random Processes • Fall 2007 Assignment No. 11; Due Thursday, November 15, 2007 Please include the following information on the first page of each assignment: (1) Your name (printed legibly), (2) Course number EE 351K , (3) Assignment Number , and (4) Due Date . Thank you. Problem 1 Consider the following pdf. otherwise x ae x f x X 0 0 ) ( 3 = (a) Evaluate “a” so that ) ( x f X is a correct pdf (b) Calculate ] [ X E (c) Calculate ] [ X V (d) Calculate X σ (Standard Deviation) (e) Calculate the CDF Problem 2 Consider the following joint pdf otherwise y x y x f Y X 1 0 0 2 ) , ( , < < < = (a) Find the marginal distributions ) ( x f X and ) ( y f Y (b) Find ] [ X E and ] [ Y E (c) Find ] [ X V and ] [ Y V (d) Find ) | ( | y x f Y X and ) | ( |
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Unformatted text preview: x y f X Y (e) Are X and Y independent? (f) Find ] | [ y Y X E = and ] | [ x X Y E = , and then ] [ X E and ] [ Y E from the conditional expectations (g) Find [ ] 2 / 1 | 2 / 1 = ≤ ≤ Y X P (h) Find the covariance of X and Y , ] , [ Y X Cov (i) Find the correlation coefficient, Y X , ρ Problem 3 Consider the following joint pmf for r.v.’s X and Y . Y X 2 4 1 0.3 0.4 3 0.1 0.2 Find (a) ) ( x p X and ) ( y p Y (b) ] [ X E and ] [ Y E (c) ] [ X V and ] [ Y V (d) ) | ( | y x p Y X and ) | ( | x y p X Y (e) Are X and Y independent? (f) ] | [ y Y X E = and ] | [ x X Y E = , and then ] [ X E and ] [ Y E from the conditional expectations (g) ] , [ Y X Cov (h) Y X , ρ...
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This note was uploaded on 01/20/2010 for the course EE 351k taught by Professor Bard during the Spring '07 term at University of Texas at Austin.

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EE351KHW_11Fall2007 - x y f X Y(e Are X and Y independent(f Find | y Y X E = and | x X Y E = and then X E and Y E from the conditional

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