20092ee132B_1_hw1

20092ee132B_1_hw1 - U CLA Electrical Engineering Department...

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UCLA Electrical Engineering Department EE132B HW Set #1 Professor Izhak Rubin Problem 1 Let X denote a geometric random variable with parameter ( 29 1 0,1 p - such that ( 29 ( 29 1 n P X n p p = = - for n = 0, 1,… 1) Calculate the mean directly. 2) Calculate the variance directly. 3) Calculate the moment generating function (Z-transform). 4) Using the moment generating function, derive the mean and the variance. Problem 2 Let X denote an exponential random variable with parameter ( 29 0, λ . The probability density function for X is given by ( 29 x X f x e - = for x > 0. 1) Calculate the mean directly. 2) Calculate the variance directly. 3) Calculate the moment generating function (Laplace transform). 4) Using the moment generating function, derive the mean and the variance. Problem 3 Show that the sum of two independent Poisson random variables has a Poisson distribution. Let X and Y denote two Poisson random variables with parameter X and Y , respectively. Assume that
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20092ee132B_1_hw1 - U CLA Electrical Engineering Department...

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