Probability

Consider two continuous random variables X and Y with joint PDF uniform over the shaded region in Figure 2: (0,1) (1,1) (1, 0.5) y = (0,0) Figure 3: the joint PDF of X and Y (a) Find the conditional PDF frix(ylx). (b) Find the least mean-squared error (LMS) estimator of Y based on X. (c) Find the linear least mean-squared error (LLMS) estimator of Y based on X. (d) Now suppose that in addition to observing X , you are also told that Y 2 . Find the LMS and LLMS estimators of Y based on both X and {Y 2 -}