Probability and Decisions - The University of Texas at Austin [PDF]

In general we want to use probability to address problems involving more than one .... each of these states had a 50-50

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Section 1: Introduction, Probability Concepts and Decisions

Carlos M. Carvalho The University of Texas at Austin McCombs School of Business http://faculty.mccombs.utexas.edu/carlos.carvalho/teaching/ Suggested Reading: Naked Statistics, Chapters 1, 2, 3, 5, 5.5 and 6 OpenIntro Statistics, Chapters 2 and 3

1

Getting Started

I

Syllabus

I

General Expectations 1. Read the notes 2. Work on homework assignments 3. Be on schedule

2

Course Overview

Section 1: Introduction, Probability Concepts and Decisions Section 2: Learning from a$'%( '23('$%Q

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pr (S = 7PA 4, E = 1)+> 0.175 !Q !!"# U > !pr Q (E = 1) = 0.7 = 0.25 !$# 7P> !Q !" 21

pr (S = 4|E = 1) =

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Conditional, Joint and Marginal Distributions Example... Given S = 4 what is the probability of E = 1?

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pr (E = 1|S = 4) =

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pr (S = 4, E = 1) 0.175 = = 0.745 pr (S = 4) 0.235

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22

Independence Two random variable X and Y are independent if pr (Y = y |X = x) = pr (Y = y ) for all possible x and y . In other words, knowing X tells you nothing about Y !

e.g.,tossing a coin 2 times... what is the probability of getting H in the second toss given we saw a T in the first one? 23

Trump’s victory

Let’s try to figure out why were people so confused on November 8th 2016... I am simplifying things a bit, but starting the day, Trump had to win 5 states to get the presidency: Florida, North Carolina, Pennsylvania, Michigan and Wisconsin. One could also say that each of these states had a 50-50 change for Trump and Hillary. So, based on this information, what was the probability of a Trump victory? (Homework: make sure to revisit this at home. )

24

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