Problem 1. Two measurements y1 = 2 and y2 = 5 are taken to estimate the value x of a random variable X. Assume that the joint distribution of the full random vector (X, Y1, Y2) is Gaussian and that X has expectation ux = 3, variance of = 4, and the following covariances with the random variables Y1 and Y2 which describe the first and second measurement, cov( X, Y1) = -1 and cov( X, Y2) = +1. Also suppose the measurements Y1 and Y2 have means My, = MY, = 3, variances of, = 3 and of, = 5 and covariance cov(Y1, Y2) = -2. Find the best mean square estimate for X in terms of these measurements