An insurance company pays out claims on its life insurance policies in accordance with a Poisson...
An insurance company pays out claims on its life insurance policies in accordance with a Poisson process rate λ = 5 per week. If the amount of money paid on each policy is exponentially distributed with mean $2000, what is the mean and variance of the amount of money paid by the company over a 4-week period?
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An insurance company pays out claims on its life insurance
policies in accordance with a Poisson...
4. A life insurance saleswoman sells on average 3 life insurance policies per week. Assume that...
4. A life insurance saleswoman sells on average 3 life insurance policies per week. Assume that the number of life insurance policies per week follows a Poisson distribution. Find the probability that in a given week, the saleswoman will sell (a) (4 points) At least 1 policy. (b) (4 points) 2 or more, but fewer than 5 policies
An insurance salesperson sells an average of 3 life insurance policies per week. Suppose insurance policies...
An insurance salesperson sells an average of 3 life insurance policies per week. Suppose insurance policies sales occur according to a Poisson distribution. a) What is the probability they will sell 3 or more policies in four weeks? b) What is the expected value of policies sold in four weeks? c) What is the variance in the expected number of policies sold?
The number of claims in a year, N, on an insurance policy has a Poisson distribution...
The number of claims in a year, N, on an insurance policy has a Poisson distribution with mean 0.25. The numbers of claims in different years are mutually independent. Calculate the probability of 3 or more claims over a period of 2 years
Annual claims filed by a policy holder of an insurance company have a Poisson distribution with...
Annual claims filed by a policy holder of an insurance company have a Poisson distribution with mean 0.4. The number of claims filed by two different policy holders are independent events. What is the probability that at least three out of ten policy holders each file at least one claim in a year?
(5 marks) Consider an account of money that an insurance company has available to pay insurance...
(5 marks) Consider an account of money that an insurance company has available to pay insurance claims, where the balance changes continuously over time according to the following rules: .The balance increases continuously at a constant rate of $2,000/day as premiums are collected The balance drops when a claim is paid out, where claim amounts, X, are Exponentially distributed with a mean of $1,000. The time to wait until the next claim, Y, is Exponentially distributed with a mean of...
An insurance company has issued 100 policies. The number of claims filed under each policy follows a Poisson distribution with a mean 2. Assuming that the claims filed by each policyholder are in...
An insurance company has issued 100 policies. The number of claims filed under each policy follows a Poisson distribution with a mean 2. Assuming that the claims filed by each policyholder are independent of each other, what is the approximate probability that more than 220 claims will be filed by the group of policyholders? B) 0.159 A) 0.079 C) 0.444 D) 0.556 E) 0.921 Question 2-20 An actuary is studying claim patterns in an insurer's book of business. He compiles...
Question 3-6 An insurance company each policy follows a Poisson distribution with a mean 3. has issued 75 policies. The number of claims filed under Assuming that the claims filed by each policyh...
Question 3-6 An insurance company each policy follows a Poisson distribution with a mean 3. has issued 75 policies. The number of claims filed under Assuming that the claims filed by each policyholder are independent of each other, what is the approximate probability that more than 250 claims will be filed by the group of policyholders? A) 0.048 B 0.168 C) 0.424 D) 0.576 E) 0.952 Question 3-7 650X and let X have the following probability density function: Let Y...
1. Many insurance policies carry a deductible provision that states how much of a claim a...
1. Many insurance policies carry a deductible provision that states how much of a claim a person must pay out of pocket before the insurance company pays the remaining of the expenses. For example, if someone files a claim for $350 on a policy with a $200 deductible, he or she pays $200 and the insurance company pays $150. In the following cases, determine how much a person would pay with and without an insurance policy. Complete parts (a) and...
An insurance company issues 1250 vision care insurance policies. The number of claims filed by a...
An insurance company issues 1250 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a random variable with u=2 and = 72. Assume the numbers of claims filed by different policyholders are mutually independent. Calculate the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?
Understanding universal life insurance Universal life insurance combines elements from term and whole life insurance. Term...
Understanding universal life insurance Universal life insurance combines elements from term and whole life insurance. Term policies provide a death benefit _______ savings component, whole life policies provide a death benefit _______ savings component, and universal policies provide a death benefit _______ savings component. To understand how universal premiums are allocated, consider the following example. Kathy is a 37-year-old lawyer who has taken out a universal life insurance policy to protect her two children (ages 8 and 6) in the...
4. A life insurance saleswoman sells on average 3 life insurance policies per week. Assume that the number of life insurance policies per week follows a Poisson distribution. Find the probability that in a given week, the saleswoman will sell (a) (4 points) At least 1 policy. (b) (4 points) 2 or more, but fewer than 5 policies
(5 marks) Consider an account of money that an insurance company has available to pay insurance claims, where the balance changes continuously over time according to the following rules: .The balance increases continuously at a constant rate of $2,000/day as premiums are collected The balance drops when a claim is paid out, where claim amounts, X, are Exponentially distributed with a mean of $1,000. The time to wait until the next claim, Y, is Exponentially distributed with a mean of...
An insurance company has issued 100 policies. The number of claims filed under each policy follows a Poisson distribution with a mean 2. Assuming that the claims filed by each policyholder are independent of each other, what is the approximate probability that more than 220 claims will be filed by the group of policyholders? B) 0.159 A) 0.079 C) 0.444 D) 0.556 E) 0.921 Question 2-20 An actuary is studying claim patterns in an insurer's book of business. He compiles...
Question 3-6 An insurance company each policy follows a Poisson distribution with a mean 3. has issued 75 policies. The number of claims filed under Assuming that the claims filed by each policyholder are independent of each other, what is the approximate probability that more than 250 claims will be filed by the group of policyholders? A) 0.048 B 0.168 C) 0.424 D) 0.576 E) 0.952 Question 3-7 650X and let X have the following probability density function: Let Y...
1. Many insurance policies carry a deductible provision that states how much of a claim a person must pay out of pocket before the insurance company pays the remaining of the expenses. For example, if someone files a claim for $350 on a policy with a $200 deductible, he or she pays $200 and the insurance company pays $150. In the following cases, determine how much a person would pay with and without an insurance policy. Complete parts (a) and...
An insurance company issues 1250 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a random variable with u=2 and = 72. Assume the numbers of claims filed by different policyholders are mutually independent. Calculate the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?
Understanding universal life insurance Universal life insurance combines elements from term and whole life insurance. Term policies provide a death benefit _______ savings component, whole life policies provide a death benefit _______ savings component, and universal policies provide a death benefit _______ savings component. To understand how universal premiums are allocated, consider the following example. Kathy is a 37-year-old lawyer who has taken out a universal life insurance policy to protect her two children (ages 8 and 6) in the...
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