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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)

#### Top Answer

The best way to approach your question... View the full answer

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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