covariance of variables: joint density fcn f(x,y)=2e^(-x-y)

[taz]

Can someone give me a hint with this question, please?

Let X and Y have a joint density function f(x,y)=2e^(-x-y), 0<x<y<infinity

(a) are they independent?
(b) find their marginal density functions
(c) Find their covariance


btw, covarians is defined by
cov(X,Y) = E[(X-E[X])(Y-E[Y])]=E[XY]-E[X]E[Y]

Thanks

 

[bilalrouf]

If i understand your question


a) they are not independent.
b) find the derivative with respect to x.

 

[JakeD]

Re: covariance of variables: joint density fcn f(x,y)=2e^(-x

Can someone give me a hint with this question, please?

Let X and Y have a joint density function f(x,y)=2e^(-x-y), 0<x<y<infinity

(a) are they independent?
(b) find their marginal density functions
(c) Find their covariance


btw, covarians is defined by
cov(X,Y) = E[(X-E[X])(Y-E[Y])]=E[XY]-E[X]E[Y]

Thanks

Do you recall that independence means the joint density can be written as the product g(x)h(y) of the marginal densities g(x) and h(y)? Can you do that here?