A company that services refrigerators in residences and convenience stores is interested in scheduling its technicians in the most efficient manner. Let the random variable X, takes the values 1, 2, 3 & 4 and denotes the service time in hours and the random variable Y, takes the values 1, 2 & 3 and denotes the number of refrigerator units. Consider the following joint p.m.f of X and Y given below
Y (No.of
X (Service time)
1
2
3
4
1
0.12
0.08
0.07
0.05
2
0.08
0.15
0.21
0.13
3
0.01
0.01
0.02
0.07
(a) is the given distribution a valid joint distribution? Justify. If valid, find the Marginal distributions of X and Y.
(b) Also, find Cov(X,Y) and comment on the independency of the variables
(3 marks)
(3 marks)