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Problem

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Textbook Expert
Textbook ExpertVerified Tutor
17 Nov 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.

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

 

Hence, the graph can be drawn as below,

 

 

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