Determine $$k$$ such that $$F$$ is a distribution function:
$$F(x,y)=kxy(2x+3y)$$, where $$x+y le 1, x 0, y 0$$

Question

Determine $$k$$ such that $$F$$ is a distribution function:
$$F(x,y)=kxy(2x+3y)$$, where $$x+y le 1, x > 0, y > 0$$

anonymous · Answer

That is,
$$F(x,y)=kxy(2x+3y),  x + y \le 1, x>0, y>0$$

zarkon · Answer

Solve
$$\int\limits_{0}^{1}\int\limits_{0}^{1-x}kxy(2x+3y)dydx=1$$

for k

the limit on the inner integral is 1-x (LaTeX need to be fixed)

myininaya · Answer

it looks fine to me

anonymous · Answer

Will try that.  The limit was confusing me on that.

zarkon · Answer

you can see the 1-x ?

myininaya · Answer

yes

zarkon · Answer

hmmm...I cannot

myininaya · Answer

satellite you can see it right?

anonymous · Answer

Looks fine to me too

myininaya · Answer

refresh your page maybe zarkon?
but gj on setting the problem up 
i knew it something to do with 1

zarkon · Answer

I'm using firefox (6.0beta) though I also had this issue with firefox v5

anonymous · Answer

i can see it.  total has to be one good job!.  i think inner integral is 
$$kx(x-1)^2$$ but my integration stinks.

zarkon · Answer

I refresh and I still have the same issue

zarkon · Answer

you are correct satellite

anonymous · Answer

Not sure if any of you are still around, but I have a follow-up to this question.  Took a break for lunch, and now I think I misunderstood the original question.  The method given above would work if this were a probability density function, but the function given above is a cumulative distribution function.  To use the method described above, would I first need to find the density function?

zarkon · Answer

that's what I would do

anonymous · Answer

Would the density function be$$k(4x+6y)$$
I'm second-guessing myself here...

zarkon · Answer

yes

anonymous · Answer

Ok.  Thank you.