b Now consider random variables X Y and Z The conditional covariance of X and Y given Z is defined by cov X YZEXEXZYEYZZx2212x2212 Show that cov YZEXYZEXZEYZ Sho ID: 293113
Download Pdf The PPT/PDF document "(a). If random variable X and Y are iden..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
(a). If random variable X and Y are identically distributed, not necessarily independent, show that: cov(,)0XYXY (b). Now consider random variables X, Y and Z. The conditional covariance of X and Y, given Z, is defined by cov(,)[([])([])] X YZEXEXZYEYZZ=−− Show that cov(,)[][][] YZEXYZEXZEYZ Show that cov(,)[cov(,)]cov([],[]) X YEXYZEXZEYZ(Hint: take the expectation of both sides of the result in part i) Z XY and error. You should express the optimal values of and in terms of variances and covariances of the random variables. y } is given by the following difference equation: kkk y aybye whereare constants and { y ii. Using results in part a, determine the linear least squares estimate of y given 1k y and 2k y . Solution 8 2.