1. ## Joint pdf Problem

Hi,

I have been given a joint pdf for 2 random variables:

f(x,y) = k - y , 0 < y < $\displaystyle x^2$< 1

and am trying to find the value of the constant k. I was just wondering if anyone could tell me whether i have set up the integral correctly. This is how i have set it up:

$\displaystyle \int_0^1 \int_0^{x^2} k-y \ dy dx \ = 1$

any help would be really apprectiated

2. Originally Posted by Number Cruncher 20
Hi,

I have been given a joint pdf for 2 random variables:

f(x,y) = k - y , 0 < y < $\displaystyle x^2$< 1

and am trying to find the value of the constant k. I was just wondering if anyone could tell me whether i have set up the integral correctly. This is how i have set it up:

$\displaystyle \int_0^1 \int_0^{x^2} k-y \ dy dx \ = 1$

any help would be really apprectiated

3. Thanks for the help!

4. Originally Posted by Number Cruncher 20
Hi,

I have been given a joint pdf for 2 random variables:

f(x,y) = k - y , 0 < y < $\displaystyle x^2$< 1

and am trying to find the value of the constant k. I was just wondering if anyone could tell me whether i have set up the integral correctly. This is how i have set it up:

$\displaystyle {\color{red}2}\, \int_0^1 \int_0^{x^2} k-y \ dy dx \ = 1$

any help would be really apprectiated
My mistake .... the red 2 should be there.

5. Thanks for the help. I think ive got it now.

6. ## the double integral

Hello. Could you explain please why the red 2 should be there? Could you post the calculation of the integral? Thanks in advance

7. Originally Posted by dely84
Hello. Could you explain please why the red 2 should be there? Could you post the calculation of the integral? Thanks in advance
Yeah, I didn't think the 2 was needed, but rather what you did in the first place.

8. Originally Posted by dely84
Hello. Could you explain please why the red 2 should be there? [snip]
Originally Posted by Richnfg
Yeah, I didn't think the 2 was needed, but rather what you did in the first place.
$\displaystyle 0< x^2 < 1 \Rightarrow -1 < x < 1$. Therefore the region of the xy-plane for which the pdf is non-zero is the region bounded by x = -1, x = 1 and $\displaystyle y = x^2$.

Originally Posted by dely84
[snip]Could you post the calculation of the integral? Thanks in advance
The integration is routine. What part can't you do?

9. Ah, I see!