# Expected value of frequency

Please help me solve this problem (and show all the work please so that I know how to complete similar problems) thank you.

1) You are a risk manager of ABC company and you are reevaulating your insurance contract. Your insurer has informed you that the expected value of frequency per month for ABC is 2.43. You believe this information is wrong and ask your CRO for the past data. You believe that the expected value of fequency per year is 2.5. (please note that the values below are on a yearly basis).

# of building losses per year Probability

0 0.35

1 0.25

2 0.15

3 0.1

4 0.05

5 0.1

1)

A) What is the correct expected value of frequency? Explain your answer.

( if you dont mind, please for the following questions (B,C,D) please use and show the correct value for expected value and frequency)

B) Calculate the variance. What are the units?

C) Calculate the standard deviation. What are the units?

D) Calculate the coefficient of variation. What are the units?

2) Now assume that when building losses do occur, they are non-random and equal to $15,000

A) Calculate he expected loss per year.

B) Calculate the expected loss per month.

C) If ABC has 45 buildings with the same distribution, calculate the expected loss per month for ALL buildings.

Thank you very much for your help

#### Solution Preview

1a) To find expected value, we multiply probability by building losses for each possible number of losses, and add the results. Expected value = .35(0) + .25(1) + .15(2) + .1(3) + .05(4) + .1(5) = 1.55.

1b) To calculate variance, we take the sum of the squared differences (between the expected value and each number of losses per year) weighted ...

#### Solution Summary

The expected value of frequency is examined. The variances and units are calculated.