There is one 1$ bill and one 5$ bill in your left pocket andthree 1$ bills in your right pocket. You move one bill from theleft pocket to the right pocket. After that you take one theremaining bill from the left pocket and one of the bills at randomfrom your right pocket. Let ? denote the amount of money that youtake from the left pocket and ? denote the amount of money that youtake from the right pocket.
1. ? (?=1, ? =1) is
(a) 1
(b) 3 (correct)
(c) 1
(d) 5
2. ? (?=5, ? =5) is
(a) 0 (correct)
(b) 1/8
(c) 3/8
(d) 1/2
3. ?(? ≥?)is
(a) 1/8
(b) 3/8
(c) 1/2 (correct)
(d) 1
4. Covariance between ? and ? is
(a) 0
(b) −1/2
(c) −1 (correct)
(d) 1
5. Let ? denote the total amount of money that you get from yourpockets. V??(?) is
(a) 23/4
(b) 31/8
(c) 19/4
(d) 15/4 (correct)
6. Let ? denote the share of money that you get from the leftpocket, i.e. ?/? . Calculate the mean of ?
(a) 1/2
(b) 2/3
(c) 11/13
(d) 5/8 (correct)
