20105ee132B_1_hw2

20105ee132B_1_hw2 - UCLA Electrical Engineering Department...

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UCLA Electrical Engineering Department EE132B HW Set #2 Professor Izhak Rubin Problem 1 For the Gaussian distribution with mean and variance 2 , find the moment generating function. Using the moment generating function, calculate the mean and the variance. Hint: The probability density function for a Gaussian random variable x with mean and variance 2 is given by   2 2 1 2 2 1 2 x X f x e   . Problem 2 Consider the following probability density function:   2 x X e fx for   , x    . 1) Find the mean directly. 2) Find the variance directly. 3) Find the moment generating function. 4) Find the mean and the variance from the moment generating function. Problem 3 A coin is flipped until heads occur twice. Define two random variables X and Y to be the trial numbers at which the first and the second heads are observed. Assume that at any trial, the probability that a head occurs is   0,1 p .
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This note was uploaded on 01/12/2011 for the course EE 132B taught by Professor Izhakrubin during the Fall '09 term at UCLA.

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20105ee132B_1_hw2 - UCLA Electrical Engineering Department...

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