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Chapter 5: Q.5.12 (page 336)

Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. If a bulb has already lasted 12 years, find the probability that it will last a total of over 19 years.

Short Answer

Expert verified

The probability that it will last a total of over 19years is0.4169.

Step by step solution

01

Given information 

The longevity of a light bulb is exponential with a mean lifetime of eight years.

02

Solution 

The required probability can be written as P(x>19鈭�x>12).

We need to use the memory less property of exponential distribution.

P(x>t+r鈭�x>t)=P(x>r)

So,

P(x>19鈭�x>12)=P(x>12+7鈭�x>12)

=P(x>7)

=1鈭�P(x鈮�7)

=1鈭�1鈭�e鈭�18脳7

=e鈭�18脳7

=0.4169

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