# The Exponential Distribution - PowerPoint PPT Presentation

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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 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.

Density function

μ= mean

e = 2.71828

### The Exponential Distribution

Cumulative probabilities

Where x0 is some specific value of x

### 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.

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### 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.)

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

Using Excel to ComputeExponential Probabilities

• Formula Worksheet

Using Excel to ComputeExponential Probabilities

• Value Worksheet

### 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

(a)

(b)

(c)

(d)

(e)