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Unformatted text preview: Connexions module: m16816 1 Continuous Random Variables: The Exponential Distribution * Susan Dean Barbara Illowsky, Ph.D. This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License † Abstract This module introduces the properties of the exponential distribution, the behavior of probabilities that re ect a large number of small values and a small number of high values. The exponential distribution is often concerned with the amount of time until some speci c event occurs. For example, the amount of time (beginning now) until an earthquake occurs has an exponential distribution. Other examples include the length, in minutes, of long distance business telephone calls, and the amount of time, in months, a car battery lasts. It can be shown, too, that the amount of change that you have in your pocket or purse follows an exponential distribution. Values for an exponential random variable occur in the following way. There are fewer large values and more small values. For example, the amount of money customers spend in one trip to the supermarket follows an exponential distribution. There are more people that spend less money and fewer people that spend large amounts of money. The exponential distribution is widely used in the eld of reliability. Reliability deals with the amount of time a product lasts. Example 1 Illustrates the exponential distribution: Let X = amount of time (in minutes) a postal clerk spends with his/her customer. The time is known to have an exponential distribution with the average amount of time equal to 4 minutes. X is a continuous random variable since time is measured. It is given that μ = 4 minutes. To do any calculations, you must know m , the decay parameter. m = 1 μ . Therefore, m = 1 4 = 0 . 25 The standard deviation, σ , is the same as the mean. μ = σ The distribution notation is X ~Exp ( m ) . Therefore, X ~Exp (0 . 25) ....
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This note was uploaded on 05/19/2011 for the course IE 2 taught by Professor A during the Spring '11 term at University of the Philippines Diliman.
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