ps6 - ECE 804 Random Signal Analysis Nov 6 2009 OSU Autumn...

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Unformatted text preview: ECE 804, Random Signal Analysis Nov. 6, 2009 OSU, Autumn 2009 Due: Nov. 16, 2009 Problem Set 6 Problem 1 Show that E[ X ] is the value (of z ) that minimizes E[( X- z ) 2 ]. Problem 2 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?...
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ps6 - ECE 804 Random Signal Analysis Nov 6 2009 OSU Autumn...

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