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Unformatted text preview: Suppose we want to determine a probability distribution that models the number of accidents that occur on I-635 in a given hour, or given week. We can think of the time interval as being broken into n sub-intervals such that P(one accident in a sub-interval) = p P(no accidents in a sub-interval) = 1 – p Here we assume the same probability p across all sub-intervals. If we let X i be 1 if an accident occurs in a given sub-interval, and 0 otherwise. We have a sequence of Bernoulli Trials, each of which are independent from each other. Let X n be the sum of these Bernoulli trials. Then X n has a Binomial distribution. This random variable is not very interesting to look at. However, as the number of sub-intervals increases, we can assume that p converges to 0....
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