# Math Help - Bivariate problem need help asap

1. ## Bivariate problem need help asap

The joint Pdf of a bivariate Rv xy

Fxy(X,Y)= {k(xy).............0<y<2x<2
0...................otherwise

K a constant

Here you will first neeb to identify and delineate properly the triangle above which pdf is not zero????

What does this mean???

Also find K
find marginal pdfs of x and y

2. Originally Posted by kermit
The joint Pdf of a bivariate Rv xy

Fxy(X,Y)= {k(xy).............0<y<2x<2
0...................otherwise

K a constant

Here you will first neeb to identify and delineate properly the triangle above which pdf is not zero????

What does this mean???

Also find K
find marginal pdfs of x and y
It means draw the region defined by 0 < y < 2x < 2. The region is the area bounded by the x-axis and the lines y = 2x and x = 1.

3. Can you let me know if this is correct

$
\int_{y=0}^{y=2}\int_{x= \frac{y}{2}}^{x=1}k(xy) \ dx \ dy = 1
$

Thanks

4. Originally Posted by kermit
Can you let me know if this is correct

$
\int_{y=0}^{y=2}\int_{x= \frac{y}{2}}^{x=1}k(xy) \ dx \ dy = 1
$

Thanks
The setup is correct.

5. $
k\int_{0}^{2}\left[\left({\dfrac{x^2y}{2}}\right)\right]_{\frac{y}{2}}^{1} \ dy=1
$

$
k\int_{0}^{2} \left( \frac{y}{2} - \frac{(y/2)^2 y}{2}\right) \ dy=1
$

Please sort out the next piece of LaTeX yourself - CB

$
k[({\dfrac{y}{\cfrac{2}{2}})^2 }-({\dfrac{y}{\cfrac{2}{\cfrac{2}{3}}}})^3 {\dfrac{y}{2}}^2]_{0}^{2}=1
$

can anyone tell me if this is integrated correctly. or have i gone wrong somewhere please

6. Originally Posted by kermit

$
k\int_{0}^{2}\left[\left({\dfrac{x^2y}{2}}\right)\right]_{\frac{y}{2}}^{1} \ dy=1
$

$
k\int_{0}^{2} \left( \frac{y}{2} - \frac{(y/2)^2 y}{2}\right) \ dy=1
$

Please sort out the next piece of LaTeX yourself - CB

$
k[({\dfrac{y}{\cfrac{2}{2}})^2 }-({\dfrac{y}{\cfrac{2}{\cfrac{2}{3}}}})^3 {\dfrac{y}{2}}^2]_{0}^{2}=1
$

can anyone tell me if this is integrated correctly. or have i gone wrong somewhere please
Not likely as no one is going to be able to parse your final expressions without working out the real answer, and then they still won't know if that is what you intended.

It would also have been nice if you had said what $f(x,y)$ was earlier.

CB

7. Originally Posted by kermit

$
k\int_{0}^{2}\left[\left({\dfrac{x^2y}{2}}\right)\right]_{\frac{y}{2}}^{1} \ dy=1
$

$
k\int_{0}^{2} \left( \frac{y}{2} - \frac{(y/2)^2 y}{2}\right) \ dy=1
$
<---

Please sort out the next piece of LaTeX yourself - CB

$
k[({\dfrac{y}{\cfrac{2}{2}})^2 }-({\dfrac{y}{\cfrac{2}{\cfrac{2}{3}}}})^3 {\dfrac{y}{2}}^2]_{0}^{2}=1
$

can anyone tell me if this is integrated correctly. or have i gone wrong somewhere please
Life would be easier if you simplified your expressions before continuing to integrate.

After simplifying the line I labelled <--- you have $k \int_0^2 \frac{y}{2} - \frac{y^3}{4} \, dy = 1$ and you shouldn't need re-assurance on how to finish this.