## anonymous 5 years ago if the joint probability density of X and Y is given by f(x,y)= .25(2x+y) for 0<x<1, 0<y<2 and 0 elsewhere I need to find the marginal density of X.............I am not sure if I am supposed to use the 0<x<1 or the 0<y<2 for the integral...if someone could answser that then I know how to do the rest of it

1. anonymous

its a double integral so take the integral with respect to x with the limits of x and then take that answer and do a second integral with respect to y and use those limits

2. anonymous

since I'm only looking for the marginal density of X the book says g(x)=$\int\limits_{?}^{?}$f(x,y)dy for $-\infty$<x<$\infty$....so its not a double integral in this case...but when I did the problem i used the 0<x<1 but my answer was incorrect, so I'm thinking that maybe i should've used the 0<y<2...any suggestions?

3. anonymous

ok wow I didn't know it was going to start a new paragraph everytime I used the equation editor

4. anonymous

i would try that since your taking integral with respect to y

5. anonymous

It is a double integral first evaluate the integral of y, then evaluate the integral of x$\int\limits_{0}^{1}\int\limits_{0}^{2}(1/2x+1/4y)dydx$