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Project1_sol_f08

Project1_sol_f08 - ECE547Project#1Fall2008 1a...

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ECE 547 Project #1 – Fall 2008 1a) 1b) P(U > x) for values of x (0.5,1) can be plotted as the following: Figure 1 P(U>x) In order to calculate P (U>x) , the interval [0, 1] is divided into intervals of width 0.01. For each value of x i the corresponding frequency f i out of a total of N= 10 5 numbers such that U> x i was calculated. Then using P (U> x i ) = f i / N, the probabilities were calculated at each of the x i .. The pairs of points ( x i , P (U> x i ) ) were plotted Note that P(U>x) = 1 x. The plot is as expected. 2a) Generation of Exponentially Distributed Random Numbers The cumulative distribution function of the exponentially distributed random variable is 0 ( ) ( ) x X X F x f x dx = where ( ) x X f x e λ λ = is the pdf of the exponentially distributed random variable with parameter λ . Choose a function G ( ) such that
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