Mathematics, 06.04.2021 04:40 Arealbot
Let Y = X + N, where X is the input, N is the noise, and Y is the output of a system. Assume that X and N are independent random variables. It is given that E[X] = 0, Var[X] = σ 2 X, E[N] = 0, Var[N] = σ 2 N . (a) Find the correlation coefficient rho between the input X and the output Y . (b) Suppose we estimate the input X by a linear function g(Y ) = aY . Find the value of a that minimizes the mean squared error E[(X − aY ) 2 ]. (c) Express the resulting mean squared error in terms of η = σ 2 X/σ2 N .
Answers: 2
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Calculate the average rate of change over the interval [1, 3] for the following function. f(x)=4(5)^x a. -260 b. 260 c. 240 d. -240
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Let Y = X + N, where X is the input, N is the noise, and Y is the output of a system. Assume that X...
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