504_hw1 - EE 504 Homework #1 Due: March 11, 2005 P.1: We...

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Unformatted text preview: EE 504 Homework #1 Due: March 11, 2005 P.1: We have studied the estimation of r.v. x from r.v. y in the last lectures. In one of the examples, the estimator had the form b x = ay + b . The minimum MSE for this estimator is derived as J ∗ = ρ 2 x (1 − ρ 2 xy ). We have noted in class that it is possible to reach zero error for this estimator (estimation matches the true value) if the correlation coefficient of x and y is ± 1. In this problem we examine the reverse argument. Show that if x and y have the correlation coefficient of ± 1, x has to be in the form x = ay + b , matching the structure of the estimator. P.2: We have derived the optimal MSE estimator as ϕ ( x ) = E { y | x } , where y is the r.v. to be estimated, x is the observation. Assume that the observation x on unknown r.v. y can take four different values, x ∈ { 1 , 2 , 3 , 4 } . We denote MSE estimator which minimizes the error E { ( y − c ( x )) 2 } by c ( x ) = E { y | x } ....
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504_hw1 - EE 504 Homework #1 Due: March 11, 2005 P.1: We...

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