Homework Answers
Solution :
Given that ,
= 0.1
Mean = 1 /
= 1 / 0.1 = 10
Option B)
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Consider an insurance policy that reimburses annual hospital charges for an insured individual. The probability of...
1. (3 POINTS) An insurance policy pays a individual $500 per day for up to 3...
1. (3 POINTS) An insurance policy pays a individual $500 per day for up to 3 days of hospitalization and $100 per day for each day of hospitalization thereafter. The number of days of hospitalization is a random variable X with P(X=x) = (6-x)/15, if x = 1,2,3,4,5. Calculate the expected payment for hospitalization under this policy. 2. (4 POINTS) An insurance policy reimburses a loss up to a benefit limit 0f $10. There is no deductible. The policyholder’s...
An individual purchases a $82,000 term life insurance with an annual payment of $620. The probability...
An individual purchases a $82,000 term life insurance with an annual payment of $620. The probability that the individual will survive the year is 0.999157. Find the expected value of the policy for the insurance company. Show your work to receive credit
Suppose a company charges an annual premium of $450 for a fire insurance policy. In case...
Suppose a company charges an annual premium of $450 for a fire insurance policy. In case of a fire claim, the company will pay out an average of $100,000. Based on actuarial studies, it determines that the probability of a fire claim in a year is 0.004. What is the expected annual profit of a fire insurance policy for the company? What annual profit can the company expect if it issues 1000 policies?
Suppose a company charges an annual premium of $140 for an insurance policy for minor injuries....
Suppose a company charges an annual premium of $140 for an insurance policy for minor injuries. Actuarial studies show that in case of an injury claim, the company will pay out an average of $900 for outpatient care and an average of $3000 for an overnight stay in the hospital. They also determine that, on average, each year there are five claims made that result in outpatient care for every 1000 policies and three claims made that result in an...
Insurance. The annual premium for a $15,000 insurance policy against the theft of a painting is...
Insurance. The annual premium for a $15,000 insurance policy against the theft of a painting is $250. If the empirical) probability that the painting will be stolen during the year is .01, what is your expected return from the insurance company if you take out this insurance? a. Let X be the random variable for the amount of money received from the insurance company in the given year. Complete the payoff table for the random variable X. (Enter the values...
Suppose a life insurance company sells a $150,000 one-year term life insurance policy to a 19-year-old...
Suppose a life insurance company sells a $150,000 one-year term life insurance policy to a 19-year-old female for $220. The probability that the female survives the year is 0.999554, Compute and interpret the expected value of this policy to the insurance company The expected value is $ . (Round to two decimal places as needed.) Which of the following interpretation of the expected value is correct? O A. The insurance company expects to make an average profit of $153.10 on...
2. Consider an individual whose utility function over income I is U(I), where U is increas-...
2. Consider an individual whose utility function over income I is U(I), where U is increas- ing smoothly in I and is concave (in other words, our basic assumptions throughout this chapter). Let Is be this person's income if he is sick, let 1н be his income if he is healthy, let p be his probability of being sick, let EI be expected income, and let ElU] be his expected utility when he has no insurance. Assum e 0 <...
Insurance companies collect annual payments from homeowners in exchange for paying to rebuild houses that burn...
Insurance companies collect annual payments from homeowners in exchange for paying to rebuild houses that burn down. a) Why should one be reluctant to accept a $300 payment from one's neighbor to replace his house should it burn down during the coming year? b) Why can an insurance company make that offer? a) Choose the correct answer below. O A. It would be foolish to insure one's neighbor's house for $300 because although one would probably collect $300, there is...
1. The size of claims made on an insurance policy are modelled through the following distribu- ti...
ANSWER QUESTION 2
1. The size of claims made on an insurance policy are modelled through the following distribu- tion: λ+1 You are interested in estimating the parameter λ > 0, using the following observations 120, 20, 60, 70, 110, 150, 220, 160, 100, 100 (a) Verify that f is a density (b) Find the expectation of the generic random variable X, as a function of when > 1 (c) Prove that the method of moments estimator of λ is...
Suppose you are selling car insurance. You have a customer with the utility function U(w)=600-200 Where...
Suppose you are selling car insurance. You have a customer with the utility function U(w)=600-200 Where w is the customer's wealth. With probability 0.1, this customer is going to get into an accident while driving. If there is an accident, the customer would have to pay for all the damages and would end up with wealth of $1. The customer has a 0.9 probability of not getting into an accident, and if this were to happen, the individual would get...
Suppose a company charges an annual premium of $140 for an insurance policy for minor injuries. Actuarial studies show that in case of an injury claim, the company will pay out an average of $900 for outpatient care and an average of $3000 for an overnight stay in the hospital. They also determine that, on average, each year there are five claims made that result in outpatient care for every 1000 policies and three claims made that result in an...
Insurance. The annual premium for a $15,000 insurance policy against the theft of a painting is $250. If the empirical) probability that the painting will be stolen during the year is .01, what is your expected return from the insurance company if you take out this insurance? a. Let X be the random variable for the amount of money received from the insurance company in the given year. Complete the payoff table for the random variable X. (Enter the values...
Suppose a life insurance company sells a $150,000 one-year term life insurance policy to a 19-year-old female for $220. The probability that the female survives the year is 0.999554, Compute and interpret the expected value of this policy to the insurance company The expected value is $ . (Round to two decimal places as needed.) Which of the following interpretation of the expected value is correct? O A. The insurance company expects to make an average profit of $153.10 on...
2. Consider an individual whose utility function over income I is U(I), where U is increas- ing smoothly in I and is concave (in other words, our basic assumptions throughout this chapter). Let Is be this person's income if he is sick, let 1н be his income if he is healthy, let p be his probability of being sick, let EI be expected income, and let ElU] be his expected utility when he has no insurance. Assum e 0 <...
Insurance companies collect annual payments from homeowners in exchange for paying to rebuild houses that burn down. a) Why should one be reluctant to accept a $300 payment from one's neighbor to replace his house should it burn down during the coming year? b) Why can an insurance company make that offer? a) Choose the correct answer below. O A. It would be foolish to insure one's neighbor's house for $300 because although one would probably collect $300, there is...
ANSWER QUESTION 2
1. The size of claims made on an insurance policy are modelled through the following distribu- tion: λ+1 You are interested in estimating the parameter λ > 0, using the following observations 120, 20, 60, 70, 110, 150, 220, 160, 100, 100 (a) Verify that f is a density (b) Find the expectation of the generic random variable X, as a function of when > 1 (c) Prove that the method of moments estimator of λ is...
Suppose you are selling car insurance. You have a customer with the utility function U(w)=600-200 Where w is the customer's wealth. With probability 0.1, this customer is going to get into an accident while driving. If there is an accident, the customer would have to pay for all the damages and would end up with wealth of $1. The customer has a 0.9 probability of not getting into an accident, and if this were to happen, the individual would get...
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