Chapter 9 - Making Hard Decisions R. T. Clemen, T. Reilly...

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Unformatted text preview: Making Hard Decisions R. T. Clemen, T. Reilly Chapter 9 – Theoretical Probability Models Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 1 of 47 COPYRIGHT © 2006 by GWU Draft: Version 1 Theoretical Probability Models Chapter 9 aking Hard ecisions R. T. Clemen, T. Reilly Making Hard Decisions R. T. Clemen, T. Reilly Chapter 9 – Theoretical Probability Models Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 2 of 47 COPYRIGHT © 2006 by GWU Draft: Version 1 Theoretical Models Applied Theoretical Probability Models may be used when they describe the physical model "adequately" Examples: 1. The outcome of an IQ test - Normal Distribution . 2. The lifetime of a component exhibiting aging - Weibull Distribution . 3. The length of a telephone call - Exponential distribution. 4. The time between two people arriving at a post office - Exponential distribution . 5. The number of people arriving at a post office in one hour - Poisson Distribution . 6. The number of defectives in releasing a batch of fixed size - Binomial distribution . Making Hard Decisions R. T. Clemen, T. Reilly Chapter 9 – Theoretical Probability Models Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 3 of 47 COPYRIGHT © 2006 by GWU Draft: Version 1 The Binomial Distribution Assumptions: 1. A fixed number of trials, say N. 2. Each trial results in a “Success” or “Failure” 3. Each Trial has the same probability of success p. 4. Different Trials are independent. Define: X = “# Successes in a sequence of N trials”, ( , ) X B N p ⇔ ∼ ( , ) P r ( | , ) ( 1 ) , x N x N X B N p X x N p p p x − ⇔ = = ⋅ − ∼ 0,1, , x N = " Making Hard Decisions R. T. Clemen, T. Reilly Chapter 9 – Theoretical Probability Models Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 4 of 47 COPYRIGHT © 2006 by GWU Draft: Version 1 The Binomial Distribution )! ( ! ! x N x N x N − ⋅ = ! ( 1) ( 2) ( 3) 4 3 2 1 N N N N N = ⋅ − ⋅ − ⋅ − ⋅ ⋅ ⋅ " : N x • # of ways you can choose x from a group of N • E[X] = N*p • Var(X) = N*p*(1-p) Making Hard Decisions R. T. Clemen, T. Reilly Chapter 9 – Theoretical Probability Models Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 5 of 47 COPYRIGHT © 2006 by GWU Draft: Version 1 The Binomial Distribution DUAL RANDOM VARIABLE OF X: X = “# Successes in a sequence of N trials”, Y = “# Failures in a sequence of N trials”, Y = N-X Pr( | ,1 ) Pr( | , ) P r ( | , ) Y y N p N X y N p X N y N p = − = − = = = − y N y y N N y N p p y N p p y N N − − − − ⋅ − = − ⋅ − = ) 1 ( ) 1 ( ) ( Making Hard Decisions R. T. Clemen, T. Reilly Chapter 9 – Theoretical Probability Models...
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This note was uploaded on 01/26/2010 for the course ADMS 3300 taught by Professor Shamimabdullah during the Spring '10 term at York University.

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Chapter 9 - Making Hard Decisions R. T. Clemen, T. Reilly...

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