Question

In order to set premiums at profitable levels, insurance companies must estimate how much they will have to pay in claims on cars of each make and model, based on the value of the car and how much damage it sustains in accidents. Let C be a random variable that represents the cost of claims on a randomly selected car of one model. The probability distribution of C is given below.

C $0 $500 $1000 $2,000
P(C) 0.60 0.05 0.13 0.22
1. The expected value of C is:____.
a. $155
b. $595
c. $875
d. $645
e. $495
2. Which of the following is the best interpretation of the expected value E(C)?
a) If the company insures 10 cars of this model, they know they will incur 10xE(C) in costs.
b) The company must insure at least E(C) of these cars to make a profit.
c) If the company insures a large number of these cars, they can expect the variability in cost per car to average approximately E(C).
d) The maximum cost to the company for insuring this car model is E(C) per car.
e) If the company insures a large number of these cars, they can expect the average cost per car to be approximately E(C).

Answer 1

$595

e) If the company insures a large number of these cars, they can expect the average cost per car to be approximately E(C).

Explanation:

Given the distribution :

C $0 $500 $1000 $2,000

P(C) 0.60 0.05 0.13 0.22

Expected probability : E(C)

Σ[C * P(C)] = (0*0.60) + (500*0.05) + (1000*0.13) + (2000*0.22) = $595

Since the expected value could be interpreted as the average value of a random variable over a large Number of experiment or trials