Transcribed Image Text From This Questionlet X And Y Be Two Jointly Normally Distributed Random Variables Such That Of O 1 (28.99 KiB) Viewed 67 times
Transcribed Image Text from this QuestionLet X and Y be two jointly normally distributed random variables such that of Oxy (~)--(C):(. ) > where o} > 0,0 > 0 and Cov(X,Y) = Oxy = Oyx. Decide whether the following statements are true/false. Note: Two continuous random variables X and Y with joint density fx.y and marginal densities fx. fy are independent if (for all x,y) fxy(x, y) = fx(x). fy). Moreover, fx.x(x, y) = xix(y|x)fx(x). True False o X and Y are independent, if Snix(y|x) = fx(*) Corr(YX) = O Let X, Y be uncorrelated, then Y| XNwy, o) o Let X, Y be correlated, then oxy € (0.1) o O o o Vary) = (0) -C Oxy 3) () It follows that Y ~ N(of). o YN (1,6) and Y|X ~ N(My, ) imply that X, Y are independent
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) > where o} > 0,0 > 0 and Cov(X,Y) = Oxy = Oyx. Decide whether the following statements are true/false. Note: Two continuous random variables X and Y with joint density fx.y and marginal densities fx. fy are independent if (for all x,y) fxy(x, y) = fx(x). fy). Moreover, fx.x(x, y) = xix(y|x)fx(x). True False o X and Y are independent, if Snix(y|x) = fx(*) Corr(YX) = O Let X, Y be uncorrelated, then Y| XNwy, o) o Let X, Y be correlated, then oxy € (0.1) o O o o Vary) = (0) -C Oxy 3) () It follows that Y ~ N(of). o YN (1,6) and Y|X ~ N(My, ) imply that X, Y are independent