ps7 - ECE 804, Random Signal Analysis OSU, Autumn 2008 Nov....

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ECE 804, Random Signal Analysis Nov. 10, 2008 OSU, Autumn 2008 Due: Nov. 17, 2008 Problem Set 7 Problem 1 We want to obtain the mold content per volume, m , of the water in the Dreese building, with an error that, with 95 % probability, is less than 0 . 1. The technique we use for this measurement has an error that is random with mean 0 and standard deviation 2. So, we can model our measurements as X i = m + N i , where N i is the noise in measurement i , with a mean of 0, and a std. deviation of 2. The N i ’s are independent for i = 1 , 2 , . . . . In order to reduce the error, we perform a number of measurements and compute their average: M n = 1 n n X i =1 X i (a) Find the mean and the variance of M n . (b) Suppose we model M n as a Gaussian random variable. With this approximation, what is the number of measurements needed to achieve the desired reliability? (c) Using the Chebychev Inequality, ±nd an upper bound on the number of measurements we need to achieve the reliability goal. Problem 2
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ps7 - ECE 804, Random Signal Analysis OSU, Autumn 2008 Nov....

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