Neural net.LetY=X+Z, where the signalXUnif[1,1] and noiseZN(0,1) are independent. We want to estimate sgn(X), where

1x0

W. We assume thatWis independent of with zero mean, unit variance,

sgn(x) =

+1x>0.

(a) Find the functiong(y) that minimizes MSE =E(sgn(X)g(Y))2.

Express your answer in terms of the cumulative distribution function ofN(0,1)z1x2

(b) Plotg(y) as a function ofy.

Neural net. Let Y = X + Z, where the signal X ~ Unif[-1, 1] and noise Z ~ N(0, 1) are independent. We want to estimate sgn(X), where -1 x0. (a Find the function g(y) that minimizes MSE = E[(sgn(X) - g(Y) ) 2]. Express your answer in terms of the cumulative distribution function of N(0, 1) 2 2 $ ( 2 ) 4 e 2 dx. V2TT (b) Plot g(y) as a function of y