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The random vector [x y]' has pdf fx,y(x,y)=k exp{-2x^2-3xy-9/2y^2} where k is some constant Find E(x) var(y) cov(x,y) corr(x,y)

The random vector [x y]' has pdf
fx,y(x,y)=k exp{-2x^2-3xy-9/2y^2} where k is some constant
Find E(x) var(y) cov(x,y) corr(x,y)

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552241_STAT.docx

Here, ……(1)
Now, joint density of bivariate normal is
……(2)
Comparing (1) and (2) we get,
So, E(X)=0, E(Y)=0
Var(X)=1/3, Var(Y)=4/27
Corr(X,Y)= -0.5
Cov(X,Y) = corr(X,Y)SD(X) SD(Y) = -0.5 *...

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