# Math Help - Conditional density function

1. ## Conditional density function

A number x is an element [0, infinity] is selected so as to have an exponential distribution with parameter alpha >0, that is fx(X) = alpha* e^-alpha*x for all x>=0 and zero otherwise. Once X = x is chosen, a second number Y is select so that it is uniformly distributed on the interval [ x, x+ beta] for soe constant B > 0.

Calculate the conditional density function of f[y|x=x](y)?
Ok so i knwo the formula for this is fx,y(x,y)/fy(y) but i have no idea where to get the y part....

The answer is given by 1/beta....

2. I'd bet that you really want to find X|Y
since it looks like we know that Y|X is uniform (X,X+B)

3. Hi,thanks for replying!

No its definitely Y|x=x
The way i see to do it...after looking at a few examples is X+B - X = B
and then put 1 over this....seems to work for the majority of the examples i have.....

4. THIS READ AS a conditional...

Once X = x is chosen, a second number Y is select so that it is uniformly distributed on the interval [ x, x+ B] for some constant B > 0

This should be $f_{Y|X}(y|X=x)={1\over B}$ when $x\le y\le x+ B$.