5. ISE has installed a new air purifying system in all 25 lecture rooms, one per room. Suppose 2 of them are defective. If the lifetime of a good air purifier is exponentially distributed with mean 5 years and only 1 year for a defective one. (a) Find the chance that one of the installed air purifiers lasts for more than 3 years. (b) If an installed air purifier has lasted for more than 3 years, find the probability that it will last for another 3 years. (c) Write the expression for the probability that at least 8 of the installed air purifiers last for more than 3 years, then estimate the value.
5. ISE has installed a new air purifying system in all 25 lecture rooms, one per room. Suppose 2 of them are defective. If the lifetime of a good air purifier is exponentially distributed with mean 5 years and only 1 year for a defective one. (a) Find the chance that one of the installed air purifiers lasts for more than 3 years. (b) If an installed air purifier has lasted for more than 3 years, find the probability that it will last for another 3 years. (c) Write the expression for the probability that at least 8 of the installed air purifiers last for more than 3 years, then estimate the value.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:5. ISE has installed a new air purifying system in all 25 lecture rooms, one per room.
Suppose 2 of them are defective. If the lifetime of a good air purifier is exponentially
distributed with mean 5 years and only 1 year for a defective one.
(a) Find the chance that one of the installed air purifiers lasts for more than 3 years.
(b) If an installed air purifier has lasted for more than 3 years, find the probability that it will last
for another 3 years.
(c) Write the expression for the probability that at least 8 of the installed air purifiers last for
more than 3 years, then estimate the value.
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