Chapter 3--Random Variables

Chapter 3--Random Variables -...

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98f655069e809f55a1c6bd57f7fcc16c769c92fa.doc STATISTICS 301—APPLIED STATISTICS, Statistics for Engineers and Scientists, Walpole, Myers, Myers, and Ye, Prentice Hall Goal: In this section we will tackle the concept of RANDOM VARIABLES , an important concept in statistics. Defn : A random variable (RV) is a method of assigning one and only one number to the outcome of an experiment. Notation : Upper Case Latin letters are used to denote random variable , eg X, or Y, or F. Lower case Latin letters are used to denote the VALUE of the RV , eg x’s, y’s, f’s and are listed in the sample space of the RV. SOME EXAMPLES 1. Experiment consists of rolling a die (fair or otherwise) D = # dots on the top face S D = { 1, 2, 3, 4, 5, 6 } 2. Experiment consists of tossing a fair coin H = # heads S H = { 0, 1 } 3. Experiment consists of selecting a student randomly from class ID = Miami ID/Banner ID S ID = { 00123456, 00123457, … } 4. Experiment consists of selecting a student randomly from class A = age (in years) S A = { 21, 22, … } //home/vdimitrov/16954/98f655069e809f55a1c6bd57f7fcc16c769c92fa.doc 4/28/2011 1
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MOTIVATION Why do we need RV’s? Recall the first day of class when we talked about populations, parameter, samples, and statistics. Further recall their definitions. Some common statistics that we deal with in statistics are Sample Average, X Sample Variance, S 2 Sample Standard Deviation, S Sample Median, X % Sample Proportion, ˆ P Note that in every case the statistic is a number associated with the outcome of a random experiment (the choosing of a particular sample)! //home/vdimitrov/16954/98f655069e809f55a1c6bd57f7fcc16c769c92fa.doc 4/28/2011 2 Parameter Population Sample Statistic Sampling Method
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SOME MORE EXAMPLES 1. The following experiment is performed: 13 cards are dealt from a well-shuffled poker deck of 52 cards. Define three different random variables for this experiment. a. X = b. Y = c. W = 2. For the following examples, determine whether the example is an example of a random variable. If it is not, explain why. If it is, give the sample space. a. A study of education followed a large group of fifth grade children to see how many years of high school they eventually completed. One student is selected at random; let X be the highest grade of high school the student completes. b. A student is randomly selected from this class. Let X be the student’s final letter grade in the course. c. A house is randomly selected from the Oxford area. Let X be the number of occupants in the house. d. A car is randomly selected from Butler County. Let X be the make of the car. e. A student is selected from this class.
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This note was uploaded on 04/27/2011 for the course ACCT 2311 taught by Professor Bcd during the Spring '11 term at University of Houston.

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Chapter 3--Random Variables -...

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