Let \(X\) and \(Y\) have joint density
\[ f(x,y) = c e^{-2x -3 y} \quad (x,y>0)\]
for some \(c>0\) and \(f(x,y)=0\) otherwise. find:
- the correct value of \(c\).
- \(P( X \leq x, Y \leq y)\)
- \(f_X(x)\)
- \(f_Y(y)\)
- Are \(X\) and \(Y\) independent ? Explain your reasoning ?
