The number of successful claims on life insurance policies for an insurance company has been determined...

The number of successful claims on life insurance policies for an insurance company has been determined to follow a Poisson process with an average rate of 5 claims per week. If the amount of money paid on each policy is uniformly distributed between $2,000 and $10,000, what is the mean of the total amount of money that the company pays out in a four-week period?

Expert Solution

expected amount paid on single policy E(x)=(2000+10000)/2 =6000

expected number of polcies to be paid in 4 week E(N)=4*5 =20

therefore mean of the total amount of money that the company pays out in a four-week period =E(X)*E(N)

=20*6000=120000

orchestra answered 2 years ago

An insurance company issues 1600 vision care insurance policies. The number of claims filed by a...

An insurance company issues 1600 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 5. Assume the numbers of claims filed by distinct policyholders are independent of one another. Find the approximate probability that the number of total claims during a one-year period is between 7928 and 8197.

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 Poisson random variable with mean 2. Assume the numbers of claims filed by a distinct policyholders are independent of one another. What is the approximate probability that there is a total of between 2450 and 2600 claims during a one year period?

Consider a portfolio of insurance policies, on which the number of claims has a binomial distribution...

Consider a portfolio of insurance policies, on which the number of claims has a binomial distribution with parameters n = 1,000 and p = 0.01. The claim size distribution is assumed to be exponential with mean $100. Claim amounts are assumed to be independent random variables, and the claim amounts are independent of the number of claims. The insurer takes out an individual excess of loss reinsurance contract with a retention level of $200. Calculate the mean of the aggregate...

1. The number of claims in a month for a portfolio of insurance policies is thought...

1. The number of claims in a month for a portfolio of insurance policies is thought to follow the Negative-binomial distribution with pdf ?(?) =( Γ(20+?) / Γ(? +1)Γ(20) ) . ?^20 . (1−?)^?, ? = 0,1,2,… A sample of 4 months had claim numbers of 15, 25, 20 and 21. a) There is no prior information for p. Using an uninformative prior to derive the posterior distribution for p. [12 marks] b) Show that the mode of the Beta...

An insurance company has determined that each week an average of 9 claims are filed in...

An insurance company has determined that each week an average of 9 claims are filed in its Atlanta branch. What is the probability that during the next week at least 18 claims will be filed? How to solve this problem without Excel? Thanks

An insurance company has been reviewing the performance of the different types of insurance policies it...

An insurance company has been reviewing the performance of the different types of insurance policies it sells. Looking at policies sold in 2018, the insurance company found that out of 850 car insurance policies sold, 322 had claims against them; and for the 924 home polices .sold, 260 had claims against them. i. Calculate a 95% confidence interval for the proportion of claims made against car insurance policies. ii. Calculate a 95% confidence interval for the proportion of claims made...

An insurance company has written two life insurance policies for a husband and wife. Policy 1...

An insurance company has written two life insurance policies for a husband and wife. Policy 1 pays $10,000 to their children if both husband and wife die during this year. Policy 2 pays $100,000 to the surviving spouse if either husband or wife dies during this year. The probability that the husband will die this year is .011. The probability that the wife will die this year is .008. Find the probability that each policy will pay a benefit this...

Claims arrive to an insurance company according to a Poisson Process. The average number of claims...

Claims arrive to an insurance company according to a Poisson Process. The average number of claims reported every day is 2.5. It has been reported that 15% of these claims are fake. What is the probability that in a week of five business day 10 claims arrive and one of these is fake? ONLY ANSWERRRRR

A global insurance company plans to offer life insurance policies in a developing country. It needs...

A global insurance company plans to offer life insurance policies in a developing country. It needs to estimate how many years, on average, residents of this country will live by reviewing death records of deceased individuals at a local government office. What (minimum) sample size is needed to form a 97% confidence interval to estimate the true average lifespan of residents in this country to within ±1.5 years? Assume the population standard deviation is known to be 10 years. Do...

What is the difference between Whole Life Insurance and Term life Insurance policies?

Question