3. There is one 1$ bill and one 5$ bill in your left pocket andthe same in your right pocket. You move one bill from the leftpocket to the right pocket. After that you take the remaining billfrom the left pocket and one of the bills at random from the rightpocket. Let ? denote the amount of money that you take from theleft pocket and ? denote the amount of money that you take from theright pocket. Answer the following questions.
(a) Calculate the joint PMF of ? and ? and the marginal PMF(Probability mass function)-s
(b) Are ? and ? independent?
(c) Find C??(?, ? ) and C???(?, ? )
(d) Find V??(? + ? )
(e) Let ? be the total amount of money that you take from yourpockets. Find the PMF of ?, its mean and variance
(f) Find C??(?, ?) and C???(?, ?)
