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 11.7 and the cdf in Figure 11.8.
The lifetimes for a certain brand of computer monitors are exponentially distributed with a mean ? = 4 years. Compute the probability that these monitors have lifetimes between 4 and 8 years.
Solution:
The probability P( 4 < x < 8) is computed from the cross-hatched area in Figure 11.11.
For this example,
From (11.31),
and
By substitution into (11.32),
Therefore, we can say that there is a probability of 23.3% that the monitors have lifetimes between 4 and 8 years.
The result can also be found with Excel's EXPONDIST function whose syntax is
<span class="serif">=EXPONDIST(x,lambda,cumulative)</span>
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 11.7, ? = 1/ ?
