Thread: expected value of conditional density funtion (urgent)

the joint density of X and Y is given by
f(x,y)= (e^-(x/y)*e^-y)/y 0 <x < inf , 0 < y < inf

show E(x]y=y)

so i worked out the conditional density function=
(e^-x/y )/y (confirmed to be correct)
now i need to integrate from 0 to infinity integral [x*(e^-x/y )/y dx] right???

i'm trying to integrate by parts
I cant show this to = y

Originally Posted by mtlchris

the joint density of X and Y is given by
f(x,y)= (e^-(x/y)*e^-y)/y 0 <x < inf , 0 < y < inf

show E(x]y=y)

so i worked out the conditional density function=
(e^-x/y )/y (confirmed to be correct)
now i need to integrate from 0 to infinity integral [x*(e^-x/y )/y dx] right???

i'm trying to integrate by parts
I cant show this to = y

Please show all your working and say where you get stuck.

Note: Wolfram|Alpha

Be sure to click on Show Steps.

To do the definite integral, which is an improper integral, you need to set up a limit.