1. ## Mean value

how to determine E(y) for the joint probability density function fxy(x,y)=2/19 over the range 0<x<5 and 0<y and x-1<y<x+1?

I tried determining fy for 0<y<1 (fy1) and for 6>y>1 (fy2) separating the space where fxy is defined by the line y=1 and then
I integrated y*fy1dy from 0 to 6 and then y*fy2dy from 1 to 6 is that a correct method to do it? cause I have:
fy1=(y+1)*(2/19)
fy2=(4/19)
and the result I get is not correct? can anyone see where is my mistake?

2. Originally Posted by Mppl
how to determine E(y) for the joint probability density function fxy(x,y)=2/19 over the range 0<x<5 and 0<y and x-1<y<x+1?

I tried determining fy for 0<y<1 (fy1) and for 6>y>1 (fy2) separating the space where fxy is defined by the line y=1 and then
I integrated y*fy1dy from 0 to 6 and then y*fy2dy from 1 to 6 is that a correct method to do it? cause I have:
fy1=(y+1)*(2/19)
fy2=(4/19)
and the result I get is not correct? can anyone see where is my mistake?
Draw a picture, then decompose the required integral into pieces that are easy to characterize, You should get something like:

$\displaystyle E(y)=\int_{x=0}^1\int_{y=0}^{x+1}\frac{2}{9}\;y \;dydx +\int_{x=1}^5\int_{y=x-1}^{x+1}\frac{2}{9}\;y \;dydx$

CB

3. It seems to me, and I may be mistaken, that you dont need the third integral. I mean, why didn't you go all the way from 1 to 5 in the second outer integral? And even if you wanted to split the integral why is the iner integral fom x-1 to 5? y is not limited at five I think! well plz clarify me, I would be thankfull

4. Originally Posted by Mppl
It seems to me, and I may be mistaken, that you dont need the third integral. I mean, why didn't you go all the way from 1 to 5 in the second outer integral? And even if you wanted to split the integral why is the iner integral fom x-1 to 5? y is not limited at five I think! well plz clarify me, I would be thankfull
Yes, you are right I will correct the post.

CB