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Variance and Standard Deviation - Penn Math

Variance and Standard DeviationChristopher CrokeUniversity of PennsylvaniaMath 115 UPenn, Fall 2011 Christopher CrokeCalculus 115 VarianceThe first first important number describing a probabilitydistribution is the mean or expected valueE(X).The next one is thevarianceVar(X) = 2(X). The square root ofthe Variance is called theStandard (xi) is the probability distribution function for a randomvariable with range{x1,x2,x3,..}and mean =E(X) then:Var(X) = 2= (x1 )2f(x1) + (x2 )2f(x2) + (x3 )2f(x3) +..It is a description of how the distribution spreads .NoteVar(X) =E((X )2).The Standard Deviation has the same units asX. ( ifXismeasured in feet then so is .)Christopher CrokeCalculus 115 VarianceThe first first important number describing a probabilitydistribution is the mean or expected valueE(X).The next one is thevarianceVar(X) = 2(X). The square root ofthe Variance is called theStandard (xi) is the probability distribution function for a randomvariable with range{x1,x2,x3.}

Variance and Standard Deviation Christopher Croke University of Pennsylvania Math 115 UPenn, Fall 2011 Christopher Croke Calculus 115. Variance The rst rst important number describing a probability distribution is the mean or expected value E(X).

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