1. The problem statement, all variables and given/known data Two variables, X and Y have a joint density f(x,y) which is constant (1/∏) in the circular region x2+y2 <= 1 and is zero outside that region The question is: Are X and Y independent? 2. Relevant 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)=fX(x)*fY(y) 3. 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-x2 ) to sqrt(1-x2) 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.