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 .

Gexpressions: practice question 3 of 5 jackson wants to study the popularity of his music video by tracking the number of views the video gets on his website. the expression below represents the total number of views that jackson's video receives n days after he begins tracking the nu views, where b is the rate at which the number of views changes. alb)" select the statement that would accurately describe the effect of tripling a, the initial number of views before jackson beginst the rate at which the number of views changes, b, will triple. the total number of views the video has after n days, a(b)", will not change. the total number of days since jackson begins tracking views, n, will be reduced by one-third. the total number of views the video has after n days, alb)", will triple. submit