HO2 - Problem Set 0_ Introducing Beta Distributions

HO2 - Problem Set 0_ Introducing Beta Distributions -...

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Unformatted text preview: MS&E 352 Handout #2 Decision Analysis II January 6 th , 2009 Problem Set 0 Due: January 13, 2009 ________________________________________________________________________ 1 of 6 This problem set is a gentle tutorial to the beta distribution, which we shall use extensively in this class. You will need Excel to complete the assignments. Please take a screen capture of your Excel graphs and tables for each assignment, put it in a word document and submit it on Coursework (Submit Homework). BETA DISTRIBUTION A long time ago, a mathematician developed magical powers and put a spell on his children such that they would have mathematical desires. While other children ask for gifts, these children ask for distributions. It is New Years Eve, and daddy has promised one gift for all three children. John: Daddy, I want a uniform distribution, and I want it right now. Sally: I like bell curves, please daddy, give me a bell curve. Tom: Daddy, I really want to stretch the bell curve! I love making it wide and then narrow. Daddy: Alright, alright. I will satisfy all of you. You will get the beta distribution! John: Huh? Whats a beta distribution? Daddy: It is a magical distribution that can satisfy all three desires. It has the following probability density function (pdf): 0, , ) 1 ( ) , ( 1 ) , ; ( 1 1- =-- x x B x f and B is the beta function. Sally: Whats the beta function? Daddy: It is the Euler integral of the first kind, defined by: --- = 1 1 1 ) 1 ( ) , ( dt t t y x B y x , for Re(x), Re(y) > 0 Tom: This looks quite scary Daddy! Why should we care? Daddy: Because the Beta distribution is quite powerful. It can represent uniform and bell shaped curves. The and constants define the shape and size of the curve and let us create a variety of shapes. When = = 1, you get the uniform distribution. MS&E 352...
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This note was uploaded on 06/16/2010 for the course MS&E 352 taught by Professor Ronhoward during the Winter '09 term at Stanford.

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HO2 - Problem Set 0_ Introducing Beta Distributions -...

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