Assume that United Delivery Service (UDP), a mail service company, has distribution centers all along the East coast. UDP uses a fleet of 700 delivery trucks in its operations dispersed among the various distribution centers. From past information the Chief Risk Officer for UDP has constructed the following probability distribution for the number of losses per truck per month.

# of losses per truck per month	Probability
0	0.20
1	0.15
2	0.30
3	0.27
4	0.06
5	0.02

Calculate expected value of frequency per truck per month.

Calculated the variance.

Now assume that when truck losses do occur, they are non-random and always equal to $300.

Calculate the expected loss per truck per month?

Calculate the expected loss for ALL trucks per month.

Calculate the expected loss for ALL trucks for the year.

UDP has one major competitor on the East Coast, Speedy Delivery (SD). SD has similar operations and services as does UDP. However SD has a smaller fleet of trucks, with 350 trucks dispersed throughout the region. From past information SD has collected the following data for the number of losses per truck per month.

# of losses per truck per month	# of trucks having these losses
0	110
1	90
2	70
3	???
4	30

a. As a new hire in SDs risk management department, you are asked to derive the probability distribution for frequency based on the information provided above.

Now you are an insurance underwriter, looking at submissions from both UDP and SD. You would like to know which company faces the most risk? Show/Explain how you came to this answer

From past information, SD has constructed the following distribution related to dollar amount of losses when accidents do occur.

$ amount of losses	Probability of dollar loss
200	0.50
500	0.30
1500	0.15
3000	0.05

Calculate the expected value of severity for SD.

Calculate the expected loss per truck per month.