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STAT 270 (2)
Chapter 5

stat chap 5.docx

8 Pages
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Department
Statistics
Course Code
STAT 270
Professor
Timothy Swartz

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The binomial distribution has the following properties The mean of the distributionis equal to nP x2The varianceis nP 1P xThe standard deviationis sqrt nP 1PxChapter 5 Continuous DistributionsProbability Distributions Discrete vs continuous If a variable can take on any value between two specified values it is called a continuous variable otherwise it is called a discrete variableExamples1Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds The weight of a fire fighter would be an example of a continuous variable since a fire fighters weight could take on any value between 150 and 250 pounds2Suppose we flip a coin and count the number of heads The number of heads could be any integer value between 0 and plus infinity However it could not be any number between 0 and plus infinity We could not for example get 25 heads Therefore the number of heads must be a discrete variableDiscrete probability DistributionIf a random variable is a discrete variable its probability distribution is called a discrete probability distributionContinuous Probability DistributionIf a random variable is a continuous variable its probability distribution is called a continuous probability distributionA continuous probability distribution differs from a discrete probability distribution in several ways The probability that a continuous random variable will assume a particular value is zeroAs a result a continuous probability distribution cannot be expressed in tabular formInstead an equation or formula is used to describe a continuous probability distribution Most often the equation used to describe a continuous probability distribution is called a probability density function PDF
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