TABLE OF CONTENTS The pdf of the exponential distribution is defined as
It can be shown that the mean of the exponential distribution is
and the variance is
The exponential distribution is also expressed as
By integrating the pdf, we find that the cfd of the exponential distribution is
The pdf of the exponential distribution is shown in Figure 10.7 and the cdf in Figure 10.8.
The lifetimes for a certain brand of computer peripherals are exponentially distributed with a mean = 4 years. Compute the probability that these peripherals have lifetimes between 4 and 8 years.
Solution:
The probability P(4 < x < 8) is computed from the cross-hatched area in Figure 10.9. For this example,
From (10.31), Page 10 10,
and
By substitution into (10.32), Page 10 11,
Therefore, we can say that there is a probability of 23.3% that the peripherals have lifetimes between 4 and 8 years,
The result can also be found with Excel s EXPONDIST function whose syntax is
=EXPONDIST(x,lambda,cumulative)
where
x = value of the function
lambda = the parameter value
cumulative = exponential function, If TRUE, the cdf is returned, and if FALSE, the pdf is retuned,
With the data given in Example 10.7, ? = 1/ = 1/4. Then,
=EXPONDIST(8,1/4,TRUE) returns 0.865, while=EXPONDIST(4,1/4,TRUE) returns 0.632,
The area in the interval 4 ?
