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09hw4

09hw4 - EE 464 Mitra Homework 3 Due Friday Box 8/EEB 104...

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EE 464, Mitra Spring 2009 Homework 3 Due Friday, February 13, 2009, Box 8/EEB 104 9AM This problem set investigates the definition of a random variable; the cumulative distribution function and its properties; probability mass functions and probability density functions. 1. Write out the probabilities of the events { X < a } , { X a } , { a X < b } , { a X b } , and { a < X < b } in terms of F X ( x ) and P [ X = x ] , for x = a, b . 2. Show that the conditional distribution of X given the event A = { b < X a } is given by F X ( x | A ) = 0 x b F X ( x ) - F X ( b ) F x ( a ) - F X ( b ) b < x a 1 x > a NOTE: first determine an expression for F X ( x | A ) using the definition of conditional prob- ability, then evaluate the particular distribution function for the particular definition of A . 3. The probability mass function (pmf) for the Poisson random variable is given by P [ X = k ] = e - λ λ k k ! (a) For the values λ = 0 . 1 , 1 , 10 , plot the pmf. Comment on how the pmf changes as a function of λ .

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