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Unformatted text preview: Assignment 2 Problems: 1. Illustrate the effect of undersampling x ( t ) = cos(2 πf t ) for a sampling rate of f s = 3 2 f . 2. Let X be a non-negative discrete r.v. with pmf Pr( X = i ) = p i (for i = 0 , 1 ,... ) and cdf (for x = 0 , 1 ,... ) F X ( x ) defines Pr( X ≤ x ) = x summationdisplay i =0 p i Let Y be a non-negative continuous r.v. with pdf f Y ( y ) and cdf F Y ( y ). (a) Show that E [ X ] = ∑ i ≥ p i i can also be computed in terms of the cdf with E [ X ] = ∞ summationdisplay i =0 (1- F X ( i- 1)) . Hint: Count how many times each p i appears in the standard E [ X ]. (b) Show that E [ Y ] = integraltext ∞ f Y ( y ) y dy can also be computed in terms of the cdf with E [ Y ] = integraldisplay ∞ (1- F Y ( y )) dy. 3. Using a biased coin to make an unbiased decision. Alice and Bob want to choose between the opera and the movies by tossing a fair coin. Unfortunately, the only available coin is biased and lands heads with probability p . Since they both know p , whomever calls the...
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This note was uploaded on 11/13/2011 for the course ECEN 455 taught by Professor Staff during the Spring '08 term at Texas A&M.
- Spring '08