= 6. The lifetime, in years, of an air compressor is an exponentially distributed random variable T with mean u. If the compressor is defective, its lifetime, Ta, has u 0.1 whereas if the compressor is not defective, its lifetime Tnd has mean = 1. Twenty percent of compressors are defective. [Recall that an exponential random variable with mean u has probability density function f(t) = exp{-} for t > 0.] (a) Let D(t) denote the conditional probability that a compressor is defective, given that it fails after t years of usage. Show that D(t) = 5 5+2e⁹t
= 6. The lifetime, in years, of an air compressor is an exponentially distributed random variable T with mean u. If the compressor is defective, its lifetime, Ta, has u 0.1 whereas if the compressor is not defective, its lifetime Tnd has mean = 1. Twenty percent of compressors are defective. [Recall that an exponential random variable with mean u has probability density function f(t) = exp{-} for t > 0.] (a) Let D(t) denote the conditional probability that a compressor is defective, given that it fails after t years of usage. Show that D(t) = 5 5+2e⁹t
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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6. The lifetime, in years, of an air compressor is an exponentially distributed random variable
T with mean . If the compressor is defective, its lifetime, Ta, has u : 0.1 whereas if the
compressor is not defective, its lifetime Tnd has mean = 1. Twenty percent of compressors
are defective. [Recall that an exponential random variable with mean u has probability density
function f(t) = exp{-} for t > 0.]
μ
(a) Let D(t) denote the conditional probability that a compressor is defective, given that it
fails after t years of usage. Show that
D(t)
=
5
5+2e⁹t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f76606-a4d9-42f0-be0d-7b1366a5593f%2F305824a3-909a-4e32-947b-1fbdc3509a91%2Fe0kq11b_processed.png&w=3840&q=75)
Transcribed Image Text:=
6. The lifetime, in years, of an air compressor is an exponentially distributed random variable
T with mean . If the compressor is defective, its lifetime, Ta, has u : 0.1 whereas if the
compressor is not defective, its lifetime Tnd has mean = 1. Twenty percent of compressors
are defective. [Recall that an exponential random variable with mean u has probability density
function f(t) = exp{-} for t > 0.]
μ
(a) Let D(t) denote the conditional probability that a compressor is defective, given that it
fails after t years of usage. Show that
D(t)
=
5
5+2e⁹t
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