4 Engineers often use the uniform distribution to model the arrival time of some event given that the event did occur within some interval. For example, pro- duction knows that a particular pump failed at some time between 1:00 and 3:00 P.M. Given that we know it failed at some time during this period, the pdf for the specific time within the period is f(y)= 0 otherwise where a = 1 and b = 3. This pdf essentially says that all the times within this interval are equally likely to occur. a. Derive the mean for this distribution. b. Derive the variance and the standard deviation for this distribution. c. Find the probability that the pump failed after 1:30 P.M.

4 Engineers often use the uniform distribution to model the arrival time of some event given that the event did occur within some interval. For example, pro- duction knows that a particular pump failed at some time between 1:00 and 3:00 P.M. Given that we know it failed at some time during this period, the pdf for the specific time within the period is f(y)= 0 otherwise where a = 1 and b = 3. This pdf essentially says that all the times within this interval are equally likely to occur. a. Derive the mean for this distribution. b. Derive the variance and the standard deviation for this distribution. c. Find the probability that the pump failed after 1:30 P.M.

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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