Given a joint PDF f(x,y)=6xy2f(x, y) = 6xy^2f(x,y)=6xy2 for 0≤x≤10 \le x \le 10≤x≤1 and 0≤y≤10 \le y \le 10≤y≤1, are the variables XXX and YYY independent?
Yes, because f(x,y)f(x, y)f(x,y) can be factored into g(x)h(y)g(x)h(y)g(x)h(y)
No, because the support is a rectangle
Yes, because the sum of probabilities is 1
No, because the integral is not 1