# Thread: Conditional expectations of continouous r.v.

1. ## Conditional expectations of continouous r.v.

Hi!

I have one question, which i cant get my head around:
x exponential(0.01) and y Gaussian ((X+80)/2 ,10).

Would somebody be able to explain how to calculate conditional expactation of Y given X?
It would be a huge help, thank you in advance.

2. ## maybe...

I think the f(Y|x) should look something like this and E should be y multiplied by the whole thing, and integrated over -infinity to +infinity, am i on the right way? in that case, what should i do now? the equation looks scary

3. Knowing the marginal densities does not give you the joint density UNLESS the random variables are independent.
The study of how to build joint densities from marginals is called Copulas.
http://en.wikipedia.org/wiki/Copula_(statistics)
(Abe Sklar just retired from my dept 5 years ago.)
NOW, if these rvs are indep, then $\displaystyle f(y|x)=f(y)$.
If you give me the joint density, then $\displaystyle f(y|x)={f(x,y)\over f(x)}$.