Question

Engineers in a company mananged to solve the probability linked to the annual driving ticket fee. The result was:

X (# of tickets annually)	0	1	2	3	4	5	6
P(X=x)	0.2	0.25	0.2	0.15	0.1	0.05	0.05

1. What is the expected value of X? How many tickets is expected for the average driver to have?

2.The police department decides to add a surcharge in accordance to the formula 100X². If a random person is selected,what would be the expected value of total payment for the driving ticket? If there are a million drivers, how much in earnings is expected annually for the surcharge concept?

Answer 1

1. The expected value of X =

Since the number of tickets is an integer so

2 tickets are expected for the average driver to have.

2).

Let,

the expected value of total payment for the driving ticket =

Then E(Y)=705

If a random person is selected, the expected value of the total payment for the driving ticket will be 705 units.

If there are a million drivers, the expected earning is units.