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EE351KHW_15Fall2009

# EE351KHW_15Fall2009 - π − and Calculate(a t X E(b 2 t X...

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THE UNIVERSITY OF TEXAS AT AUSTIN Department of Electrical and Computer Engineering EE 351K • Probability and Random Processes • Fall 2009 Assignment No. 15, Due Monday, November 30, 2009 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 random process ) ( t X , which is stationary ) cos( ) ( 0 θ ω + = t A t X where θ is a uniformly distributed r.v. between
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Unformatted text preview: π − and . Calculate (a) )] ( [ t X E (b) )] ( [ 2 t X E (c) )] ( ) ( [ ) ( τ + = t X t X E R X Problem 2 Consider the random process ) cos( ) ( + = t A t X , which is assumed to be stationary and ergodic. Calculate (a) > < ) ( t X (b) > < ) ( 2 t X (c) > + =< ) ( ) ( ) ( t X t X R X where > ⋅ < denotes a time average over one period, 2 = T . (d) Compare your answers for (a), (b), and (c) with the corresponding answers for Problem 1....
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