Homework Assignment # 7 ECE 251A 1. Show that E*[Y|X1, X2] : E*[Y|X1] + E*[Y|X2], when X1 and X2 are orthogonal random vectors. X1 and X2 are vectors and can have different dimensions. E*[Y|Z] denotes the best linear mean squared estimate, i.e. E*[Y|Z] : YO : (Rglezy)H Z. Then generalize it to the case where X1 and X2 are correlated. In the correlated case, show that E*(Y|X1, X2) : E*(Y|X1) + E*(Y|X2), where X2 : XgE*(X2|X1). Note that with Y : d[n], X1 : [:13[2'1],.r[77.1]7 ...,:r[n m+ INT, and X2 : [3;[nm]], we get the updating property discussed in the context of the backward prediction errors