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Unformatted text preview: Chapter 4: Discrete Random Variables and the Binomial Distribution Chapter 4: Discrete Random Variables and the Binomial Distribution Keith E. Emmert Department of Mathematics Tarleton State University June 16, 2011 Chapter 4: Discrete Random Variables and the Binomial Distribution Outline 1 Random Variables 2 Binomial Random Variables Chapter 4: Discrete Random Variables and the Binomial Distribution Random Variables Some Basic Definitions A random variable is an uncertain numerical quantity whose value depends on the random outcome of an experiment. We can think of a random variable as a rule that assigns one (and only one) numerical value to each outcome of a random experiment. A discrete random variable can assume at most a finite or infinite but countable number of distinct values. A continuous random variable can assume any value in an interval or collection of intervals. Think of the capital letter X as ::::::: random, the value of the variable before it is observed. Think of x as :::::: known, a ::::::::: particular ::::: value :: of ::: X that has been observed. Chapter 4: Discrete Random Variables and the Binomial Distribution Random Variables Lets Do It Random Variables 1 Otitis media , a disease of the middle ear, is one of the frequent reasons for visiting a doctor in the first 2 years of life other than routine wellbaby visit. Let X be the random variable that represents the number of episodes of Otitis media in the first two years of life. What are the values, x , the random variable X will assume? 2 Suppose a physician agrees to use a new antihypertensive drug on a trial basis on the first 4 untreated hypertensive patients she encounters in her practice, before deciding whether to adopt the drug for routine use. Let X be the number of patients out of 4 who are brought under control. What are the values, x , the random variable X can assume? Chapter 4: Discrete Random Variables and the Binomial Distribution Random Variables Lets Do It Random Variables 3 A study on effects of exposure to radiation was performed at the Portsmouth Naval Shipyard, where each exposed worker wore a dosimeter that measures the annual exposure in rem. The cumulative exposure over a workers lifetime could then be obtained by summing the yearly exposure. Let X be the amount of cumulative exposure. What are the values, x , the random variable X will assume? 4 A biology teacher gives a 30 minutes test. Define the random variable as the time it takes a student to finish the test. What are the values, x , the random variable X will assume? Chapter 4: Discrete Random Variables and the Binomial Distribution Random Variables Lets Do It Random Variables andom riable, X Discrete Probability mass function. Height corresponds to proability....
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This note was uploaded on 01/13/2012 for the course MATH 350 taught by Professor Keithemmert during the Summer '11 term at Tarleton.
 Summer '11
 KeithEmmert
 Binomial

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