# Week4 - Stat231 William Marshall Stat231 William Marshall...

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Stat231 William Marshall Stat231 William Marshall May 20, 2010

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Stat231 William Marshall Week 4 Goals: Look at continuous examples of MLE Introduce Gaussian response / regression models
Stat231 William Marshall Example 7 Many products have a guarenteed lifetime. In a test of a new electrical component, 20 units are selected randomly for testing. The components are used until they fail or 24 hours passes, whichever happens ﬁrst. Model: Suppose y i are i.i.d realization of Y Exp ( θ ) Data: 24.0 6.2 13.4 11.0 0.5 24.0 4.4 6.5 2.5 4.3 1.8 14.1 14.0 13.2 16.8 24.0 4.3 7.9 24.0 2.2

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Stat231 William Marshall Example 7 What is the likelihood function L ( θ )? What is the MLE ˆ θ What is the probability a product lives through its guarentee? P ( Y > t 0 )
Stat231 William Marshall Example 8 Suppose we repeatedly measure an object 3 times, because it is known that the measurement system is ﬂawed. The data is y 1 = 3 . 22, y 2 = 3 . 19, y 3 = 3 . 24. Model: The data are i.i.d realizations from

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## This note was uploaded on 11/21/2011 for the course MATH STAT 231 taught by Professor Marsh during the Spring '10 term at Waterloo.

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Week4 - Stat231 William Marshall Stat231 William Marshall...

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