# Thread: NEED HELP with joint density problem

1. ## NEED HELP with joint density problem

Two RVs X & Y have the jiont density: f(x,y)=a, x^2+y^2<=1

Find the constant a.

>>> HOW CAN I SOLVE THIS ???can i say that z=x^2+y^2

2. ## Re: NEED HELP with joint density problem

hint:

Since it is symmetric on both axis.. you can focus on first quadrant. Take one variable as free and other is depending on the free variable..

3. ## Re: NEED HELP with joint density problem

can u plz explain for me how to put the limits, should i put each in terms of the other???

4. ## Re: NEED HELP with joint density problem

You are confusing yourself by thinking this is a complicated problem.

The probablity density is just a constant, so this is a simple, uniform distribution over a region of the (x,y) plane. The equation x^2 + y^2 <= 1 is just defining that region. Just figure out what the region looks like.

There is no calculus involved here. There is no math beyond elementary school.

5. ## Re: NEED HELP with joint density problem

Originally Posted by ichbin
There is no math beyond elementary school.
You learned the equation of a circle in elementary school? Impressive...

6. ## Re: NEED HELP with joint density problem

Once you know that

represent a unit disc, then
is just the reciprocal of the area of a unit disc.

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