20082ee131A_1_HW6

20082ee131A_1_HW6 - 4 Problem 4.82(part b only p 221(3rd...

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EE 131A Homework #6 Spring 2008 Due May 14th K. Yao Read Leon-Garcia (3rd edition), pp. 155-180. 1. Let S be the speed of a randomly selected molecule in a gas. According to the kinetic theory of gases, S has the Maxwell pdf of f S ( s ) = as 2 exp( - s 2 / (2 σ 2 )) , 0 < σ, 0 < s < . a. Find the constant a. Hint: Use integration by parts. b. Denote the mass of the molecule by m and the kinetic energy of the molecule by the rv X = (1 / 2) mS 2 . Find the pdf f X ( x ) , 0 < x < . Hint: Find the new pdf f X ( x ) from the pdf f S ( s ) as the result after the transformation of X = g ( S ) where g ( s ) = (1 / 2) ms 2 . 2. Problem 4.63, p. 221 (3rd edition). 3. Problem 4.67, p. 221 (3rd edition).
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Unformatted text preview: 4. Problem 4.82 (part b only), p. 221 (3rd edition). 5. Problem 4.91, p. 223 (3rd edition). 6. Let X be a Laplacian rv with a pdf given by f X ( x ) = ( α/ 2)exp(-α | x | ) , < α,-∞ < x < ∞ . Suppose X is the input to the eight-level uniform quantizer in Fig. 4.8(a) on page 162 (3rd edition) or Fig. 3.15 on page 120 (2nd edition). Find the pmf of the quantizer output levels. Find the probability that the input X exceeds the [-4d, 4d] of the dynamic range of the quantizer....
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This note was uploaded on 04/12/2010 for the course EE 131A taught by Professor Lorenzelli during the Spring '08 term at UCLA.

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