The amount of a loss is exponentially distributed with mean 90. An insurance pays 90% of...

The amount of a loss is exponentially distributed with mean 90. An insurance pays 90% of the amount of a loss in excess of an ordinary deductible of 20. The maximum payment is 117 per loss. Determine the expected payment, given that a payment has been made.

Expert Solution

Solution:

orchestra answered 2 years ago

Suppose that an insurance company sells a policy whose losses are distributed exponentially with mean $1500....

Suppose that an insurance company sells a policy whose losses are distributed exponentially with mean $1500. Further suppose that the company sells a large number of claims. An actuary wishes to analyze the performance of the product and takes a random sample of 100 policies for which there was a claim filed from this population. a. What are the mean and variance of an individual insurance policy? b. What are the mean and variance of the total claim amount T...

Losses are uniformly distributed on [0, m]. The insurer pays the amount of loss after a...

Losses are uniformly distributed on [0, m]. The insurer pays the amount of loss after a deductible of m/5.There is a 60% chance that the insurer pays at least 200. Find the probability that the insurer pays at least 500.

Suppose we face a lossLthat is exponentially distributed with mean$10,000. We purchase an insurance policy against...

Suppose we face a lossLthat is exponentially distributed with mean$10,000. We purchase an insurance policy against this loss with a $5,000 deductible. The premium charged by the insurance companyis twice their expected payout. (a) What is the median loss? (b) What is the probability that the insurance company will have topay a claim on this policy? (c) What is the expected loss given that the loss is greater than$25,000? (d) Give an expression for the amount that the insurance companypays...

Suppose the amount of time to finish assembling a component is exponentially distributed with an average...

Suppose the amount of time to finish assembling a component is exponentially distributed with an average of 2 minutes. (a) What is the probability that it takes more than 5 minutes to assemble a component? (b) If 100 components are randomly selected, what is the probability that the average amount of time to assemble these100 components is more than 2.3 minutes?

given an exponentially distributed population with a mean of 385.06 what is the probability of the...

given an exponentially distributed population with a mean of 385.06 what is the probability of the average of 138 randomly selected items being less than 53018.8

The distance between flaws on a long cable is exponentially distributed with a mean of 12...

The distance between flaws on a long cable is exponentially distributed with a mean of 12 m. a) Find the probability that the distance between two flaws is greater than 15 m. b) Find the probability that the distance between two flaws is greater than 25 m given that it is greater than 10 m. c) Find the probability that the distance between two flaws is greater than 20 m given that it is greater than 10 m.

the time between phone calls received by a telephonist is exponentially distributed with a mean of...

the time between phone calls received by a telephonist is exponentially distributed with a mean of 10 minutes.what is the probability that there are no more than four calls within one hour?

A critical component on a submarine has an operating lifetime that is exponentially distributed with mean...

A critical component on a submarine has an operating lifetime that is exponentially distributed with mean 0.50 years. As soon as a component fails, it is replaced by a new one having statistically identical properties. What is the smallest number of spare components that the submarine should stock if it is leaving for a one-year tour and wishes the probability of having an inoperable unit caused by failures exceeding the spare inventory to be less than 0.02? Please show that...

A random variable X is exponentially distributed with a mean of 0.21. a-1. What is the...

A random variable X is exponentially distributed with a mean of 0.21. a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.) a-2. What is the standard deviation of X? (Round your answer to 2 decimal places.) b. Compute P(X > 0.36). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

Car battery The mileage of a car battery is exponentially distributed with a mean value of...

Car battery The mileage of a car battery is exponentially distributed with a mean value of 10000 km. (a) What is the probability of a 5000 km trip without replacement of the battery? (b) What is the maximum length of travel that can be terminated with 90% probability without replacing the battery? (c) Determine the median, the mean and the variance of the mileage of the battery

Question