# A bourhim syracuse university random variable

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A. Bourhim (Syracuse University)Random Variable & Probability DistributionMAT121, Spring 20153 / 10
Requirement for a probability distribution1Each probability value must be between 0 and 1:0P(x)1for any valuex.2The sum of all probabilities must be 1:XP(x)=1wherexassumes all possible values.A. Bourhim (Syracuse University)Random Variable & Probability DistributionMAT121, Spring 20154 / 10
ExampleDoes the following table determine a probability distribution?xP(x)00.0710.0920.3430.3240.18A. Bourhim (Syracuse University)Random Variable & Probability DistributionMAT121, Spring 20155 / 10
GraphsTheprobability histogramis very similar to a relative frequency histogram, butthe vertical scale shows probabilities. The bars are centered at randomvariables and their heights correspond to the probabilities.ExampleConstruct the probability histogram of the following probability distribution.xP(x)10.1620.3430.3240.18A. Bourhim (Syracuse University)Random Variable & Probability DistributionMAT121, Spring 20156 / 10
Mean, Variance and Standard Deviation; see page 200Mean(Formula 5-1) :μ=X[x.p(x)].Variance(Formulas 5-2 & 5-3) :σ2=X[(x-μ)2.P(x)]=X[x2.P(x)]-μ2.Standard deviation is the square root of the variance(Formula 5-4) :σ=sX[x2.P(x)]-μ2.