Question

United and Villa are meeting in an important football match. Based on

previous encounters and current form, the probabilities of the various scores

are given in the table below, where U and V denote the numbers of goals

scored by United and Villa respectively. Thus, the probability that United win

3-2 is 0.08. It is believed that the probabilities of either team scoring 4 or

more goals are negligible.

	V
U	Goals	0	1	2	3
	0	0.2	0.1	0.04	0.01
	1	0.1	0.08	0.06	0.03
	2	0.06	0.04	0.07	0.03
	3	0.04	0.03	0.08	0.03

1. Describe the marginal distributions of U and V respectively.
2. What is the expected number of goals scored by Villa?
3. Find E(UV) and the covariance of U and V.        
4. Calculate and interpret the correlation between U and V.
5. What is the probability of a Villa victory?
6. What is the probability of a drawn game?                        

Answer 1