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The time failure of a component in an electronic device has an exponential distribution with median of 8 hours?
The time failure of a component in an electronic device has an exponential distribution with median of 8 hours.
Calculate the probability that the component will work without failing for at least 9 hours.
Exponential distribution:
Cumulative distribution function=F(x,λ)=1-e^(-λx)
Median=ln(2)/λ
Your median is 8 hours ==>
8=ln(2)/λ ==> λ=ln(2)/8 ==>
F(x,λ)=1-e^(-x*ln(2)/8)=
=1-[e^(ln2)]^(-x/8)=1-2^(-x/8)
P(X>9 hours)=1-F(9,λ)=1-[1-2^(-9/8)]=2^(-9/8)=
=0.4585=45.85%
http://en.wikipedia.org/wiki/Exponential_distribution
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