Solution Found!
The life length Y of a component used in a complex
Chapter 4, Problem 157E(choose chapter or problem)
Problem 157E
The life length Y of a component used in a complex electronic system is known to have an exponential density with a mean of 100 hours. The component is replaced at failure or at age 200 hours, whichever comes first.
a Find the distribution function for X, the length of time the component is in use.
b Find E( X ).
Questions & Answers
QUESTION:
Problem 157E
The life length Y of a component used in a complex electronic system is known to have an exponential density with a mean of 100 hours. The component is replaced at failure or at age 200 hours, whichever comes first.
a Find the distribution function for X, the length of time the component is in use.
b Find E( X ).
ANSWER:
Solution
Step 1 of 2
a) We have to find distribution function of length of life of a component
Here X has an exponential density with mean 100 hours
The mean of exponential distribution is
Then
Component replaced at the age 200 hours
Then x=200
The pdf of exponential distribution is
=
The distribution function of X is
=
=
=
The distribution function of X is
=
=