Question

Explain in detail and give an example situation where the exponential distribution applies ?

Note: Example is MUST.

Answer 1

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The exponential distribution often involves the period of time before a given occurrence occurs. Of example, before an earthquake happens, there is an exponential distribution of the time. The frequency of long distance telephone calls in minutes and the amount of time in months for a car battery are other examples. This also appears that the amount of your cash in your pocket or bag is approximately balanced by the exponential distribution.

The values are estimated for the exponential random variable. There are less and less qualities. For example, the amount of money spent by customers on a single visit to the shop follows an exponential distribution. More people invest small amounts of cash and fewer spend big sums of cash.The exponential distribution is commonly used in the field of reliability. The time a product lasts is defined in the reliability.

EXAMPLE

Suppose that the length of a phone call, in minutes, is an exponential random variable with decay parameter = 112. If another person arrives at a public telephone just before you, find the probability that you will have to wait more than five minutes. Let X = the length of a phone call, in minutes.

What is m, μ, and σ? The probability that you must wait more than five minutes is _______ .

Solution:

m = 112112

μμ = 12

σσ = 12

P(x > 5) = 0.6592

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