The warranty on a machine specifies that it will be replaced at failure or age 5...
The warranty on a machine specifies that it will be replaced at failure or age 5 which ever occurs first. The machine's age at failure, X, has density function
f(x) = 1/7, 0 < x < 7
f(x) = 0 otherwise. Let Y be the age of the machine at the time of replacement. Calculate the expected value of Y.
Homework Answers
E(Y) =E(min(x,5)) =
min(x,5)f(x) dx =
(x/7) dx +
(5/7) dx
=(x2/14) |50 +(5x/7)|75
=(25/14)+(10/7)
=45/14
=3.21 years
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