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Means and Variances of RV 7.2

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Example # of BoysP(X) 0.0625 1.25 2.375 3.25 4.0625 Find the expected value, or mean, of the probability distribution above:

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Mean of a Discrete RV Also called the expected value, what we would expect if we took many trials Suppose X is a discrete RV whose distribution is: Value of Xx 1 x 2 x 3 …x k Probabilityp 1 p 2 p 3 …p k The mean of X is found by: – µ x = E(X) =

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Example cont. # of BoysP(X)Dev (x - µ)Dev (x - µ) 2 0.0625 1.25 2.375 3.25 4.0625 Find variance (σ 2 ) of the probability distribution above. note: variance is the expected value of the squared deviations from the mean): Find the standard deviation (σ) note: variance is standard deviation squared:

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Variance of a Discrete RV Suppose X is a discrete rv whose distribution is: Value of Xx 1 x 2 x 3 …x k Probabilityp 1 p 2 p 3 …p k And that is the mean of X. The variance of X is: The standard deviation σ x of X is the square root of the variance.

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