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Discrete RV

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

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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

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(DISCRETE) RANDOM VARIABLES Introduction Introduction to the Parameterized Distributions Binomial Poisson Other Distributions
Introduction Introduction to the Parameterized Distributions Binomial Poisson Other Distributions

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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 quarter’s 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 I a randomly chosen person is left-handed (about .085)

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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 quarter’s 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 { 0 , 1 , 1 , 0 , 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

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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). I The experiment is a randomly picked credit card recipient I What is X ? What values can X assume?

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

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