The Exponential Distribution The exponential distribution has a
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
The Exponential Distribution Cumulative probabilities Where x 0 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.
Example: Al’s Full-Service Pump Exponential Distribution f(x) P(x < 2) = 1 - 2. 71828 -2/3 = 1 -. 5134 =. 4866 . 4. 3. 2. 1 x 1 2 3 4 5 6 7 8 9 10 Time Between Successive Arrivals (mins. )
Using Excel to Compute Exponential Probabilities The EXPONDIST function can be used to compute exponential probabilities. The EXPONDIST function has three arguments: 1 st The value of the random variable x 2 nd 1/m 3 rd “TRUE” or “FALSE” the inverse of the mean number of occurrences in an interval we will always enter “TRUE” because we’re seeking a cumulative probability
Using Excel to Compute Exponential Probabilities n Formula Worksheet
Using Excel to Compute Exponential Probabilities n Value Worksheet
Relationship between the Poisson and 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 (a) (b) (c)
Exercise 27, p. 266: Continued (d) (e)
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