Solution Found!
An insurance company charges a customer an annual premium
Chapter 2, Problem 2.9.11(choose chapter or problem)
An insurance company charges a customer an annual premium of $100, and there is a probability of 0.9 that the customer will not need to make a claim. If the customer does make a claim, the amount of the claim $X has a probability density function
\(f(x)=\frac{x(1800-x)}{972,000,000}\)
for \(0 \leq x \leq 1800\). Each customer also incurs administrative costs to the insurance company of $5. If the insurance company has 10,000 customers, what is its expected annual profit? Would you expect the customers’ claims to be independent of each other?
Questions & Answers
QUESTION:
An insurance company charges a customer an annual premium of $100, and there is a probability of 0.9 that the customer will not need to make a claim. If the customer does make a claim, the amount of the claim $X has a probability density function
\(f(x)=\frac{x(1800-x)}{972,000,000}\)
for \(0 \leq x \leq 1800\). Each customer also incurs administrative costs to the insurance company of $5. If the insurance company has 10,000 customers, what is its expected annual profit? Would you expect the customers’ claims to be independent of each other?
ANSWER:Step 1 of 4
We are asked to find the expected profit of the insurance company.
Given data:
Probability density function f(x) of the amount of claim $X is:
\(f(x)=\frac{x(1800-x)}{972000000}, 0 \leq x \leq 1800\)
P(Customer will not make a claim) = 0.9
P(Customer will make a claim) = 1-P(Customer will not make a claim)= 1 - 0.9 = 0.1
Administrative costs: $5/customer
Number of customers: 10,000
Annual premiums charger: $100/customer