integrating joint probability distribution

stellina

New Member
Hi,
could you help me in compute the integral with respect to x of f(x,y)d(x,y) where f(x,y) is a joint probability distribution? I know that the integral with respect to x of f(x,y)dx is just f(y) where f(y) is the marginal distribution of y, but in the exercise I have f(x,y)d(x,y) inside the integral.
Thanks!!

BGM

TS Contributor
Try to provide the integrand $$d(x,y)f(x,y)$$ and tell us which part of the integral is difficult for you.

stellina

New Member
It is not specified. I'm just told that f(x,y) is a joint probability distribution and the solution should be that y is integrated out but I don't understand why.

BGM

TS Contributor
I am confused as well. Do the $$d(x, y)$$ just mean the usual "differentials"?

And the question just ask for the following well-known identity?

$$\int_{-infty}^{+\infty} \int_{-infty}^{+\infty} f(x,y)dxdy = 1$$