Suppose a man has a probability of 0.00194 of dying in the next four years. An insurance company charges $500 for a $100,000 life insurance four-year term policy to the man. That is, if the man dies within four years, the company must pay his estate $100,000; if he lives, the company pays nothing. Find the expected value of the profit for the company on this policy.

The clients of an insurance company had independent probability 0.03 of filing a claim in the year 2008. Suppose an agent gets a list of four random clients from among 20 random clients of the agency and that this larger list has at most two clients who filed a claim. Find the probability the agent gets at least one client who filed a claim in 2008.

The probability of a claim being filed on an insurance policy is .1, and only one claim can be filed. If a claim is filed, the amount is exponentially distributed with mean $1000. a. Determine E(Y |X = x) and var(Y |X = x). b. Use part a) to find E(Y ). c. Use part a) to find var(Y ).

a) When all factors are taken into account, an insurance company estimates that the probability of my father making a claim for damages to his pontoon boat for $5000 is 0.1, and that the probability of the pontoon boat being totally destroyed is .005. Should that tragedy happen, the company will have to pay $15,000. The company charges my father $1000 for the insurance policy. What is the expected value of this policy to my father?

b) The world famous gambler and statistics professor from Columbus, Michelle Duda, proposes the following game of chance. You roll a fair die. If you roll a 1, then Michelle pays you $25. If you roll a 2, Michelle pays you $5. If you roll a 3, you win nothing. If you roll a 4 or a 5, you must pay Michelle $10, and if you roll a 6, you must pay Michelle $15. What is the expected value of Michelle's game?

1. Given the probability of an accident is 20% if you did not have an accident last year, but the probability of an accident is 48% if you did have an accident, what is the expected value of insurance if each accident costs $10,000 and there are 100 policies at your company?

9. Which of the following statements is​ FALSE? A. The probability of financial distress depends on the likelihood that a firm will be unable to meet its debt commitments and therefore default. B. Firms whose value and cash flows are very volatile​ (for example, semiconductor​ firms) must have much higher levels of debt to avoid a significant risk of default. C. For low levels of​ debt, the risk of default remains low and the main effect of an increase in leverage is an increase in the interest tax​ shield, which has present value tau ​*​D, where tau ​* is the effective tax advantage of debt. D. Real estate firms are likely to have low costs of financial​ distress, as much of their value derives from assets that can be sold relatively easily.

Suppose there is a 5% probability (or risk) that you will get a very severe flu next year. If you get the flu, you will be admitted to the Hospital for at least a week, and in turn you will need to pay $2,000 for a hospital service and medical expenses. Keep in mind that you are risk-averse. While you can’t avoid getting the flu, you can avoid a financial loss due to the flu by buying a health insurance. You were looking for a health insurance with a price equal to your expected financial lose. The price of insurance is called actuarially fair insurance premium.

Question 1. What would the actuarially fair insurance premium (or expected financial lose) be? Make sure to calculate the actuarially fair insurance premium. Show how you calculated the actuarially fair insurance premium.

The business of selling insurance is based on probability and the law of large numbers. Consumers buy insurance because we all face risks that are unlikely but carry high cost. Think of a fire destroying your home. So we form a group to share the risk: we all pay a small amount, and the insurance policy pays a large amount to those few of us whose homes burn down. The insurance company sells many policies, so it can rely on the law of large numbers.

In fact, the insurance company sees that in the entire population of homeowners, the mean loss from fire is μ = $300 and the standard deviation of the loss is σ = $400.What are the mean and standard deviation of the average loss for 8 policies? (Losses on separate policies are independent. Round your standard deviation to two decimal places.)

What are the mean and standard deviation of the average loss for 15 policies? (Round your standard deviation to two decimal places.)

The business of selling insurance is based on probability and the law of large numbers. Consumers buy insurance because we all face risks that are unlikely but carry high cost. Think of a fire destroying your home. So we form a group to share the risk: we all pay a small amount, and the insurance policy pays a large amount to those few of us whose homes burn down. The insurance company sells many policies, so it can rely on the law of large numbers.

In fact, the insurance company sees that in the entire population of homeowners, the mean loss from fire is μ = $300 and the standard deviation of the loss is σ = $400.What are the mean and standard deviation of the average loss for 6 policies? (Losses on separate policies are independent. Round your standard deviation to two decimal places.)

What are the mean and standard deviation of the average loss for 13 policies? (Round your standard deviation to two decimal places.)

You are a relatively safe driver. The probability that you will have an accident is only 1 percent. If you do have an accident, the cost of repairs and alternative transportation would reduce your disposable income from $120,000 to $60,000. Auto collision insurance that will fully insure you against your loss is being sold at a price of $0.10 for every $1 of coverage. You are considering two alternatives: buying a policy with a $1,000 deductible that essentially provides just $59,000 worth of coverage, or buying a policy that fully insures you against damage. The price of the first policy is $5,900. The price of the second policy is $6,000. Which policy do you prefer?