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Unformatted text preview: Probability Concepts Continuous Random Variables Moments of Random Variables Joint Probability Distributions Class Exercise Some common continuous random variables Introduction to Econometrics Chapter 2: Review of Probability Corrected, with some answers Geo rey Williams [email protected] January 30, 2010 Geo rey Williams [email protected] Introduction to Econometrics Chapter 2: Review of Probab Probability Concepts Continuous Random Variables Moments of Random Variables Joint Probability Distributions Class Exercise Some common continuous random variables Random Variables A random variable is any variable whose value is unknown now but will become known at some later date. The values that a random variable can take is governed by a random process (sometimes called a data generating process or DGP ). Geo rey Williams [email protected] Introduction to Econometrics Chapter 2: Review of Probab Probability Concepts Continuous Random Variables Moments of Random Variables Joint Probability Distributions Class Exercise Some common continuous random variables Sample Space and Distribution The properties of a random variable can be described by its sample space and its probability distribution over the sample space. the sample space is the set of possible outcomes the variable can take the outcomes can be discrete or continuous e.g. toss of a coin, height of next student to walk in the room the likelihood of a RV taking a set of values is governed by the probability distribution of the RV Geo rey Williams [email protected] Introduction to Econometrics Chapter 2: Review of Probab Probability Concepts Continuous Random Variables Moments of Random Variables Joint Probability Distributions Class Exercise Some common continuous random variables Probability The probability of an event occurring has the following properties: the probability of any single event has to be between 0 and 1 the probability that some event in the sample space will occur is equal to 1. The random variable can be fully characterized by its probability distribution . The probability distribution fully details the probability of any event for a random variable. Geo rey Williams [email protected] Introduction to Econometrics Chapter 2: Review of Probab Probability Concepts Continuous Random Variables Moments of Random Variables Joint Probability Distributions Class Exercise Some common continuous random variables Discrete Random Variables For a discrete RV, the probability distribution function (pdf) is a function that assigns a probability to every possible event such that the total probability sums to 1. An example is the outcome of Tossing a coin . In this example the random variable is which side faces up after tossing the coin....
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 Fall '10
 MacroWilliams,MicroYoshi
 Normal Distribution, Probability theory, Geo1Brey Williams, Probab

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