Unformatted text preview: y and z are not necessarily statistically independent, show that E [ x | y , z ] = E [ x | y , ˆ z ] , where ˆ z = z-E [ z | y ] . 7. Let w = [ X,Y,Z ] T be a zero mean jointly Gaussian random vector with covariance matrix K w = 4 2 1 2 2 1 1 1 1 . (a) Find α such that X-αY and Y are independent. (b) What is the conditional expectation E [ X 2 | Y ]? (c) Find the probability density function (pdf) for S = X + 2 Y . (d) Find the conditional density f X | Y,Z ( Y,Z ) ....
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- Winter '10
- Probability theory, random vector, Gallager, 421 Kw, conditional density fX