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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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