The Exponential Distribution

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The Exponential Distribution
The exponential distribution has a number of
useful applications. For example, we can use it
to describe arrivals at a car wash or the time it
takes to load a truck.
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The Exponential Distribution
Density function
µ mean e 2.71828
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The Exponential Distribution
Cumulative probabilities
Where x0 is some specific value of x
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Example Als Full-Service Pump

• The time between arrivals of cars at Als
  full-service gas pump follows an exponential
  probability distribution
• with a mean time between arrivals of 3 minutes.
  Al would like to know the probability that the
  time between two successive arrivals will be 2
  minutes or less.

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Example Als Full-Service Pump

• Exponential Distribution

f(x)
P(x lt 2) 1 - 2.71828-2/3 1 - .5134 .4866
x
1 2 3 4 5 6 7 8 9 10
Time Between Successive Arrivals (mins.)
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Using Excel to ComputeExponential Probabilities

The EXPONDIST function can be used to compute
exponential probabilities.
The EXPONDIST function has three arguments
1st The value of the random variable x
2nd 1/m
the inverse of the mean number of occurrences
in an interval
3rd TRUE or FALSE
we will always enter TRUE because were seeking
a cumulative probability
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Using Excel to ComputeExponential Probabilities

• Formula Worksheet

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Using Excel to ComputeExponential Probabilities

• Value Worksheet

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Relationship between the Poissonand Exponential
Distributions
The Poisson distribution provides an appropriate
description of the number of occurrences per
interval
The exponential distribution provides an
appropriate description of the length of the
interval between occurrences
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Exercise 27, p. 266
(a)
(b)
(c)
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Exercise 27, p. 266 Continued
(d)
(e)