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Unformatted text preview: Assignment 2 Problems: 1. Illustrate the effect of undersampling x ( t ) = cos(2 f t ) for a sampling rate of f s = 3 2 f . 2. Let X be a nonnegative 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 nonnegative 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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 Spring '08
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