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# Exponential probability distribution

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The lifetime (hours) of an electronic device is a random variable with the exponential probability density function:
f(x)= 1/50 e ^-x/50 for x>=0

a. What is the mean lifetime of the device?
b. What is the probability the device fails in the first 25 hours of operation?
c. What is the probability the device operates 100 or more hours before failure?

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https://brainmass.com/statistics/probability-density-function/probability-exponential-probability-density-function-193703

#### Solution Preview

Please see the attached file.

The lifetime (hours) of an electronic device is a random variable with the exponential probability density function:

f(x)= 1/50 e ^-x/50 ...

#### Solution Summary

The following are calculated: mean lifetime of the device, the probability the device fails in the first 25 hours of operation, the probability the device operates 100 or more hours before failure.

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