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ece 153 quiz 3

ece 153 quiz 3 - Name 30L UTZOU ECE 153 Quiz No 3 November...

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Unformatted text preview: Name 30L: UTZOU ECE 153 Quiz No. 3 November ’19, 2003 The random variables X and Y are jointly Gaussian with zero mean, unit variance and correlation coefficient p . Define two new random variables as the following linear transformations on X and Y . U = X + Y V = X -Y. Obtain an explicit expression for the probability density of U and V . U‘flf are JON/m Gammon/z (“Fl/~07 are (:7 mean. fitwar opera t *4 0M G—auegmn var! . 105),. 4 U v .,_ le mow“ 0“ Karo EM:E[ZJ~EK¥J =0 ~w v ,. Err] ’ 2 : y’mxzwe ; Eflj—kY-EDZY/i + Eli/'1 Ei 1:4 +2p+t:2<t+fl) E1773 : g(yizzf+?j :: (~2Pfl , -- ~ 237's . rim =0. ' 771i: mew/29 TMT (Iii/a; “Ade/0‘0”” WT ' ~ ”40%) @4‘0’?) ,1 M Q l 1% ...
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