Discrete RV

Discrete RV - C22.0103: Statistics for Business Control:...

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Unformatted text preview: C22.0103: Statistics for Business Control: Regression and Forecasting Hong Luo Section 003, Spring 2009 Tue/Thu/Fri, 11:00 - 12:15pm, Tisch 200 Stern School of Business New York University (DISCRETE) RANDOM VARIABLES Introduction Introduction to the Parameterized Distributions Binomial Poisson Other Distributions Introduction Introduction to the Parameterized Distributions Binomial Poisson Other Distributions A Motivating Example I Let X 1 = 1 + 1 =? I Let X 2 = 1 + Y =?, where Y takes the value of the number comes up in a die roll. I Before you role the die, you know that X 2 = 7 with probability 1 6 , X 2 = 8 with probability 1 6 , and so on. I X 1 is nonrandom, while X 2 is random. What is a random variable? A random variable (RV) is something that takes on different values, depending on chance. Examples: I the lifetime of a light bulb (remember our GE vs. Philips light bulb example) I next quarters sales of Coca Cola I the proportion of Super Bowl viewers surveyed who remembered your ad I the return of the S&P 500 next year I the number of children a couple must have in order to get the first girl Examples of random variables I A random variable is the result of a random experiment in the abstract sense, before the experiment is preformed. I The value the random variable actually assumes is called an observation e.g. Next quarters sale of Coca Cola is a random variable, and the actual value of $3.521,395,576 is an observation of the RV I You can think of your data set as observations of a random variable resulting from several repetitions of a random experiment. e.g. toss a coin five times, and we get data { , 1 , 1 , , 1 } I In this sense, we associate the random variable with a population and view observations of the random variable as data. Discrete vs. Continuous RVs Discrete : I sample space is countable : finite or countably infinite I numbers in between the sample points cannot be achieved I e.g. (finite) number of girls in families with 4 children. I e.g. (countably infinite) world population 100 years from today Continuous : I if the RV can assume any value in some interval on the real number line I sample space is uncountable I e.g. weight of a randomly selected quarter pounder I e.g. result of Usain Bolt on 100 meters Credit Card Application The following is a sample of applicants for credit card I The experiment is a randomly picked application I What is X ? What values can X assume? I X is the result of credit card application I This is a binary variable, and we usually use 0 and 1 to denote the outcomes. I Is X discrete or continuous? Default Of 10,499 people whose application was accepted, 996 (9.494%) defaulted on their credit account (loan)....
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This note was uploaded on 11/07/2010 for the course ECON 0001 taught by Professor Kitsikopoulos during the Spring '08 term at NYU.

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Discrete RV - C22.0103: Statistics for Business Control:...

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