Homeowner’s Policy. An insurance company wants to design a homeowner’s policy for mid-priced homes. From data compiled by the company, it is known that the annual claim amount, X, in thousands of dollars, per homeowner is a random variable with the following probability distribution. x 0 10 50 100 200 P(X = x) 0.95 0.045 0.004 0.0009 0.0001 a. Determine the expected annual claim amount per homeowner.b. How much should the insurance company charge for the annual premium if it wants to average a net profit of $50 per policy?
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!
Homeowner’s Policy. An insurance company wants to design a homeowner’s policy for mid-priced homes. From data compiled by the company, it is known that the annual claim amount, X, in thousands of dollars, per homeowner is a random variable with the following probability distribution.
| x | 0 | 10 | 50 | 100 | 200 |
| P(X = x) | 0.95 | 0.045 | 0.004 | 0.0009 | 0.0001 |
a. Determine the expected annual claim amount per homeowner.
b. How much should the insurance company charge for the annual premium if it wants to average a net profit of $50 per policy?
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