(Solved): Suppose that three random variables \( X_{l}, X_{2} \), and \( X_{3} \) have following joint proba ...

Suppose that three random variables \( X_{l}, X_{2} \), and \( X_{3} \) have following joint probability distribution: \( f\left(x_{1}, x_{2}, x_{3}\right) \) \( =\left\{\begin{array}{cl}c x_{1}{ }^{\left(1+x_{2}+x_{3}\right)}\left(1-x_{1}\right)^{\left(3-x_{2}-x_{3}\right)} & \text { for } 0