2. Stick breaking. Given a stick of length 1, break it into two pieces at a location chosen uniform at random. Denote the breaking location by X, then X ~ Unif[0, 1). Keep the piece corresponding to the interval [X, 1). Break it again into two pieces at a location chosen uniform at random. Denote the second breaking location by Y, then YNX = x} ~ Unifla, 1). (a) Find the estimator of X given Y that minimizes the MSE E[(X - X )3]. (b) Find the conditional MSE given Y = y for the estimator you find in part (a). (c) Find the covariance Cov(X, Y). (d) Find the linear LMS estimator of X given Y. (e) Find the MSE for the estimator you find in part (d)