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. The Exponential Distribution. Density function. μ = mean e = 2.71828.

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The Exponential Distribution

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The exponential distribution

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.


The exponential distribution1

The Exponential Distribution

Density function

μ= mean

e = 2.71828


The exponential distribution2

The Exponential Distribution

Cumulative probabilities

Where x0 is some specific value of x


Example al s full service pump

Example: Al’s Full-Service Pump

The time between arrivals of cars at Al’s 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.


Example al s full service pump1

.4

.3

.2

.1

Example: Al’s Full-Service Pump

Exponential Distribution

f(x)

P(x< 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.)


The exponential distribution

Using Excel to ComputeExponential Probabilities

The EXPONDIST function can be used to compute

exponential probabilities.

The EXPONDIST function has three arguments:

1stThe value of the random variable x

2nd1/m

the inverse of the mean

number of occurrences

in an interval

3rd“TRUE” or “FALSE”

we will always enter

“TRUE” because we’re seeking a cumulative probability


The exponential distribution

Using Excel to ComputeExponential Probabilities

  • Formula Worksheet


The exponential distribution

Using Excel to ComputeExponential Probabilities

  • Value Worksheet


Relationship between the poisson and exponential distributions

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


Exercise 27 p 266

Exercise 27, p. 266

(a)

(b)

(c)


Exercise 27 p 266 continued

Exercise 27, p. 266: Continued

(d)

(e)


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