Textbook ExpertVerified Tutor
6 Dec 2021
Given information
Use the following information to answer the next three exercises. The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.
Let
Step-by-step explanation
Step 1.
It is deduced from the information given in the problem that the random variable is given by,
where
is the decay rate.
The probability density function of the exponential distribution is given as follows:
Putting the value of the decay rate , it gives
To obtain the required graph the maximum value of the probability function is calculated as follows:
Since the maximum value of the function occurs at , therefore
The graph of the di9stribution is as follows:
The cumulative distribution function is given by,
.
Putting the value of the decay rate , gives
Taking of log on both sides of the equation gives,
Therefore, the required value is
.
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