A traffic enforcer counts the number of vehicles at a specific location in the highway. In his counting, there are 420 vehicles arrived in span of 1 hour. Assuming that the arrival of vehicles is Poisson distributed, estimate the probabilities of having 7 vehicles arriving over a 30-second time interval, over the next one minutes.
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 traffic enforcer counts the number of vehicles at a specific location in the highway. In his
counting, there are 420 vehicles arrived in span of 1 hour. Assuming that the arrival of vehicles is
Poisson distributed, estimate the probabilities of having 7 vehicles arriving over a 30-second time
interval, over the next one minutes.
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