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Probability : Insurance Policy

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Someone purchases a liability insurance policy, and the probability that they will make a claim on that policy is equal to 0.1. The insurance payout is the amount of money the insurance company must pay if the holder of the policy files a claim. So, if no claim is made, then the insurance payout is just $0; however, whenever a claim is made, the amount of money on the claim, F, has an exponential distribution with mean S 1,000,000. If P is less than the maximum insurance policy payout of $2,000,000, then the insurance payout is equal to F, otherwise, the insurance payout is equal to S2000,000. What is the expected value of the insurance payout? Hint: Consider the indicator of the event "A claim is filed" and how it can be used to compute the expectation in question.

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Let X denotes the random variable representing the insurance payout.
Then X = 0 if no claim is made
= min{P, } if a claim is made
where P is the amount of ...

Solution Summary

The solution describes the method of determination of the expected value of the insurance payout using mixture probability distribution.

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Life Insurance Policy Payout Probability

The probability that Traci Muldone will die during the 10-year term of a life insurance policy is assessed by the insurance company at 1/5. Arthur Average's probability of living to the end of the 10-year period is reckoned at 95% What is the probability that at the end of the 10 years (a) both (b) one or the other, but not both is living?

Probability (Muldone dying) = 0.2 (given)
Probability (Average dying) = 1 - 0.95 (given)

Probability (both living) = 0.8 x 0.95 = 0.76 or 76%

i.e. Probability Muldone AND Average living = 76%

So what do we think is the probability of either one or the other (but NOT both) living?

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