Suppose that when you call OIT, the length of time you have to wait on hold before talking to a live person is uniformly distributed on the interval (0,10). Say that you have to call three times this month. Let Y1 be the time you have to wait on hold the first time, Y2 is the time you have to wait the second time you call, and Y3 is the time you spend on hold on the third call. (Note that random samples taken from a common distribution are independent). Let Y = max{Y, Y2, Y3}. Find P(Y < 5).
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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