7. Let's consider a small airport in which the passenger int er-arrival time is modelled by an exponent ial random variable with a mean of 10 seconds. a) What is the probability that more than 20 seconds elapsed time until a passenger has arrived? b) If there is a one-minute elapsed time without any passenger arrival, what is the prob- ability that a pa ssenger arriv es wit hin the next 12 seconds?
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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