A piece of equipment is being insured against early failure. The time from purchase until failure of the equipment is exponentially distributed with mean 10 years. The insurance will pay an amount x if the equipment fails during the first year, and it will pay 0.5x if failure occurs during the second or third year. If failure occurs after the first three years, no payment will be made. Calculate x such that the expected payment made under this insurance is 1000.
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!
A piece of equipment is being insured against early failure. The time from purchase until
failure of the equipment is exponentially distributed with mean 10 years. The insurance
will pay an amount x if the equipment fails during the first year, and it will pay 0.5x if
failure occurs during the second or third year. If failure occurs after the first three years,
no payment will be made.
Calculate x such that the expected payment made under this insurance is 1000.
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