- #1

serhannn

- 3

- 0

## Homework Statement

Two variables, X and Y have a joint density f(x,y) which is constant

**(1/∏)**in the circular region x

^{2}+y

^{2}<= 1 and is zero outside that region

The question is: Are X and Y

**independent**?

## Homework Equations

Well, I know that for two random variable to be independent, multiplication of their marginal densities must equal their joint denstiy, i.e.

**f(x,y)=f**

_{X}(x)*f_{Y}(y)## The Attempt at a Solution

My problem is I am confused about how to select the integration limits. I know how to do it when simple boundaries are given (like x<2 and y>1, etc.) but within a circular region, I just could not figuer out how to do it. Should I, for example, integrate y from -sqrt(1-x

^{2 }) to sqrt(1-x

^{2}) or is that a wrong approach? How can I select the integration limits in a circular region? Is it a better approach to convert to polar coordinates first and then integrate?

Thanks a lot for your help.