Econ 281 - Probability and Statistics Review UP

Econ 281 - Probability and Statistics Review UP -...

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Unformatted text preview: Probability and Statistics Review Introduction to Econometrics Econ 281 Spring Quarter 2007 So what is this all about??? Lets assume we want to investigate the following relationships What is the relationship between student performance and class size? What is the relationship between education and wages? Do I earn more if I drink a lot? No really ! 600 620 640 660 680 700 15 20 25 Test Scores and Student-Teacher Ratio Student-Teacher Ratio Test Scores 10 20 30 40 50 5 10 16 20 Highest Grade Attended Hourly Earning and Education Earnings per hour 12 Population vs. Sample Population (random) Samples Outcomes, Sample Space, and Events Lets assume we are dealing with a random process Number of times your computer crashes in a month Roll of a die Outcome = every mutually exclusive result of a random process is an outcome of that process. Computer crashes 1 time per month You roll a 6 Outcomes, Sample Space, and Events Sample Space = the set of all possible outcomes of a random process Computer can crash 0, 1, 2, 3, 4, 5, 6, .. times per month You can roll 1, 2, 3, 4, 5, 6 with a die Wages: 0 to infinity Outcomes, Sample Space, and Events Event = subset of the sample space consisting of one of more outcomes Event = Computer crashes no more than 4 times a month You roll a 1 or a 4 NOTE: All outcomes are events but not all events are outcomes S Events and Outcomes = OUTCOMES = EVENTS Random Variables Random Variable = numerical summary of a random process Number of times your computer crashes Number of times you roll a 6 in 10 tries 2 kinds of Random Variables (RVs) Discrete RVs = has a finite number of possible values = can only take on (discrete) set of values Continuous RVs = can take on a continuum of possible values Discrete Random Variables Binary Gender (male, female) College Graduate (yes=1/no=0) Usually coded 0/1 Multiple Values Marital Status (Multiple Values: Single, Married, Divorced, Separated) Continuous Random Variables Examples Height Weight Wages 10k time Education Probability Distribution A Probability Distribution assigns probabilities to events Example: Number of Heads in 3 coin tosses Discrete Random variable Lets see a graph = = = = = otherwise 3 X if 2 X if 1 X if X if ) ( 8 1 8 3 8 3 8 1 x f Probability Distribution 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1 2 3 Probability Distribution For a continuous random variable there are an infinite amount of possible events Every particular event has probability zero We can calculate the probability of a range of events Example: Unemployment duration P(UED<4weeks) P(2 weeks < UED < 4 weeks) Cumulative Probability Distribution The cumulative probability distribution gives the probability that a random variable is less than or equal to a particular value Example:...
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Econ 281 - Probability and Statistics Review UP -...

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