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HW5_10 - m and standard deviation σ In this case Y is said...

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Online EE 131A Homework #5 Fall 2010 Due Nov. 3rd K. Yao Read Leon-Garcia (3rd edition), pp. 148-188; 233-254. 1. Problem 4.63 (p. 221). 2. A limiter Y = g ( X ) is shown in Fig. P4.2 (p. 219). a. Find the cdf and pdf of Y in terms of the cdf F X ( x ) and pdf f X ( x ) of X. b. Find the cdf and pdf of Y if X has a Laplacian pdf. c. Find the cdf and pdf of Y if X is a Gaussian rv with mean m and standard deviation σ. d. Find the cdf and pdf of Y if the input X = b sin ( U ) , where U is uniformly dis- tributed in the interval [0 , 2 π ] . 3. Let Y = e X . a. Find the cdf and pdf of Y in terms of the cdf F X ( x ) and pdf f X ( x ) of X. b. Find the cdf and pdf of Y if X is a Gaussian rv with mean
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Unformatted text preview: m and standard deviation σ. In this case, Y is said to be a lognormal pdf. 4. An urn contains 90 $1 bills, 9 $5 bills, and 1 $50 bill. Let the rv X be the denomination of a bill that is selected at random from the urn. Find the mean m of X. What is the interpretation of the mean of X as the break-even price of a ticket for the right to draw a single bill from the urn? 5. Problem 4.39 (p. 219). In order to solve this problem, you need to solve for the parameter “c” in Problem 4.17. 6. Problem 4.48 (p. 219)....
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