Let X,YX, YX,Y have joint PDF f(x,y)=x+yf(x, y) = x+yf(x,y)=x+y for 0≤x,y≤10 \le x, y \le 10≤x,y≤1. Are XXX and YYY independent?
No, because f(x,y)≠fX(x)fY(y)f(x,y) \neq f_X(x)f_Y(y)f(x,y)=fX(x)fY(y)
Indeterminate
Yes, because the range is a square
Yes, because the integral is 1