HW6_ee464 - g x = x we achieve the Markov inequality...

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EE 464, Mitra Spring 2009 Homework 6 Sample Problems, do not turn in This problem set investigates properties of the expectation operator, and requires the calculation of moments of random variables and preliminaries for tail inequalities. 1. L-G 4.57 Determine the n ’th moment of a uniform random variable U [ a, b ] , b > a . 2. L-G 4.17 and 4.39 Determine the mean and variance of a random variable with the following pdf: f X ( x ) = c (1 - x 2 ) | x | ≤ 1 0 else Note that you need to determine the value of c . 3. Recall the bounding of a tail inequality considered in lecture. If we set
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Unformatted text preview: g ( x ) = x , we achieve the Markov inequality assuming that X is a non-negative random variable, i.e. P [ X ≥ a ] ≤ E [ X ] a L-G 4.97: Compare the Markov inequality and the exact probability for the event { X ≥ c } as a function of c for (a) X is a uniform random variable on [0 ,b ] (b) X is an exponential random variable with parameter λ (c) X is a Pareto random variable (see your text) with α > 1 (d) X is a Rayleigh random variable...
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