2 An individual is chosen from the maintenance staff of a co

2. An individual is chosen from the maintenance staff of a company. Let X be the number of years of service, and let Y be the hours of overtime worked per day. The following table gives the joint probability function of X and Y: (a) Determine the marginal probability functions of X and Y. [3] (b) Compute E(X), E(Y), Var(X), Var(Y) and Cov(X, Y). [6] (c) If the individual?s gross income G (in thousands of dollars) is given by 30 + 5X + 10Y, determine the mean and the standard deviation of G.

Solution

Given

y

x

0.5

1

1.5

1

0.2

0.2

0

2

0

0.25

0.15

3

0

0

0.2

y

x

0.5

1

1.5

1

0.2

0.2

0

0.4

2

0

0.25

0.15

0.4

3

0

0

0.2

0.2

0.2

0.45

0.35

1

E(Y)=

E(

E(

Var(x)=E(

Cov(x,y)= E(xy)- E(X) E(Y)=0.215

Mean of G is E(G)=30+5*E(x)+10*E(Y)=126.75

	y
x	0.5	1	1.5
1	0.2	0.2	0
2	0	0.25	0.15
3	0	0	0.2