Life insurance. You might sell insurance to a 20-year-old friend. The probability that a man aged 20 will die in the next year is about 0.0007. You decide to charge $2000 for a policy that will pay $1 million if your friend dies. a. What is your expected profit on this policy? b. Although you expect to make a good profit, you would be foolish to sell a single policy only to your friend. Why? c. A life insurance company that sells thousands of policies, on the other hand, would do very well selling policies on exactly these same terms. Explain why
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
20.20
Life insurance. You might sell insurance to a 20-year-old friend. The probability that a man aged 20 will die in the next year is about 0.0007. You decide to charge $2000 for a policy that will pay $1 million if your friend dies.
a. What is your expected profit on this policy?
b. Although you expect to make a good profit, you would be foolish to sell a single policy only to your friend. Why?
c. A life insurance company that sells thousands of policies, on the other hand, would do very well selling policies on exactly these same terms. Explain why
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