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

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taz

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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
 
If i understand your question


a) they are not independent.
b) find the derivative with respect to x.
 
Re: covariance of variables: joint density fcn f(x,y)=2e^(-x

taz said:
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
Click to expand...
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?
 
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