20082ee131A_1_HW7

# 20082ee131A_1_HW7 - ( n +1)(2 n +1) 6 . 4. (a.) Find the...

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EE 131A Homework #7 Spring 2008 Due May 21st K. Yao Read Leon-Garcia (3rd edition), pp. 115-116; 184-189; 233-255. 1. Let X be an exponential pdf with f X ( x ) = exp( - x ) , 0 x < . Let the new rv Y = 2 - X 3 . Find the pdf f Y ( y ) . For what values of y is f Y ( y ) deﬁned? 2. We buy cylinders with a diameter of 2 and is willing to accept diameters that are oﬀ by as much as ± 0 . 05. The factory produces a diameter that is normally distributed with μ = 2. (a). If σ = 0 . 08, what percentage will be rejected by us? (b). If the rejection rate is 20%, ﬁnd σ . 3. Find the mean and variance of the uniform discrete rv that take on values for the set { 1 , 2 ,...,n } with equal probability. You will need the following formula Σ n i =1 i = n ( n +1) 2 and Σ n i =1 i 2 = n
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Unformatted text preview: ( n +1)(2 n +1) 6 . 4. (a.) Find the mean and variance of of the Poisson rv with a parameter α. (b.) Let α = λ × t, where λ is is arrival rate of the Poisson rv and t is time. What is the interpretation of α = λ × t ? 5. Show that E { X } for a Cauchy rv X with the pdf of f X ( x ) = 1 π (1+ x 2 ) ,-∞ < x < ∞ does not exist. 6. Do Problem 4.112 on p. 225 (3rd edition). 4.112. Let G N ( z ) be the pgf for a Poisson rv with parameter α , and let G M ( z ) be the pgf for a Poisson rv with parameter β. Consider the function G N ( x ) G M ( z ). Is this a valid pgf? Is so, to what rv does it correspond?...
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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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