Question

There is one 1$ bill and one 5$ bill in your left pocket and three 1$ bills in your right pocket. You move one bill from the left pocket to the right pocket. After that you take one the remaining bill from the left pocket and one of the bills at random from your right pocket. Let ? denote the amount of money that you take from the left pocket and ? denote the amount of money that you take 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 your pockets. 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 left pocket, i.e. ?/? . Calculate the mean of ?
(a) 1/2

(b) 2/3

(c) 11/13

(d) 5/8 (correct)

Answer 1