Hi all,

I read recently that for any three continuous random variables, X,Y and Z, the conditional densities are related by the following formula:

$p(x|y) = \int g(x| z) h(z | y ) dz $

where $p(x|y)$ is conditional density of X given Y = y and so on.

I have never come across this relation before. It seems similar to Chapman-Kolmogorov equation but the paper I found this relation in claims it is true for any 3 continuous random variables. Can anyone provide a proof of the above relation please?

Thanks.