The number of hospital stays required for a patient with a certain condition follows a Poisson distribution with a mean of 2.8 stays per year. One such patient takes out an insurance policy to help her pay for potential hospital bills. The policy does not pay anything for the first two hospital stays in a given year, but pays 550 for each stay beyond the second. Find the expected amount paid by this insurance 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!
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