申論題

(14%) Let X and Y be two jointly distributed random variables with the joint PDF as follows:

 For some reason, samples of random variable X can be observed, but not for random variable Y. It is desired to estimate Y based on the observation of X.

(a) (7%) Find the best linear estimate (i.e. aX +b with a, b being constants to be de termined) of Y given X such that the mean square estimation error is minimized. What is the minimum mean square error thus found?