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3 Random Variables

# 3 Random Variables - BUAD 310 Applied Business Statistics 1...

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August 30, 2010 BUAD 310: Applied Business Statistics 1

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Outline for Today Random variables Density curves 2
A Quick Review Boxplot (invented by John Tukey) you commonly see: the whiskers extend out to the farthest points that are within 1.5×IQR of the quartiles Q1 and Q3 outliers are plotted individually Percentile: the value such that a specified percentage of the measurements in a population or sample fall at or below it the first quartile Q1 = 25th percentile the third quartile Q3 = 75th percentile Tolerance interval: an interval of numbers that contains a specified percentage of the individual measurements in a population ( such as 68.26 percent, 95.44 percent, or 99.73 percent ) 3

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Random Variables Will the price of a stock go up or down? Need language to describe processes that show random behavior (such as stock returns) “Random variables” are the main components of this language 4
Random Variables Definition of a Random Variable Describes the uncertain outcomes of a random process Denoted by capital letter, e.g., X Defined by listing all possible outcomes and their associated probabilities E.g., proportion of Super Bowl viewers surveyed who viewed an ad, day-trading profits for next year, number of additional children a couple with one boy must have in order to get the first girl We associate the random variable with a population and view observations of the random variable from a sample as data 5

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Random Variables Example: Suppose a day trader buys one share of IBM Let X represent the change in price of IBM She pays \$100 today, and the price tomorrow can be either \$105, \$100 or \$95 How X is Defined 6
Random Variables Two Types: Discrete vs. Continuous Discrete random variable: possible values can be counted change in price of IBM given in last slide, number of defective units in a batch of 20 Continuous random variable: may assume any numerical value in one or more intervals Waiting time for a credit card authorization, interest rate charged on a business loan 7

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Discrete Probability Distributions The probability distribution of a discrete random variable is a table, graph, or formula that gives the probability associated with each possible value that the variable can assume. Denote by x the value of a discrete r.v. and by p ( x ) its associated probability. Properties: For any value x of the r.v., p ( x ) 0 The probabilities of all possible values must sum to 1, that is, 8 ( 29 1 = x x p all
Discrete Random Variables “Long run frequency” interpretation of probability: Suppose P (event)= p . Define As n increases, this fraction will approach p : Mean (expected value) of a discrete r.v.

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3 Random Variables - BUAD 310 Applied Business Statistics 1...

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