Risky Assets

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Hal Varian Intermediate Microeconomics Chapter Thirteen Risky Assets Mean of a Distribution x A random variable (r.v.) w takes values w1,…,wS with probabilities π 1,...,π S (π 1 + · · · + π S = 1). The mean (expected value) of the distribution is the av. value of the r.v.; S E[w] = µ w = ∑ wsπ s. s=1 x Variance of a Distribution x The distribution’s variance is the r.v.’s av. squared deviation from the mean; S 2 2 var[w] = σ w = ∑ (ws − µ w) π s. x Variance measures the r.v.’s variation.
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    Hal VarianIntermediate MicroeconomicsChapter Thirteen Risky Assets    Mean of a Distribution x A random variable (r.v.) w  takesvalues w  1 ,…, w  S with probabilities π 1 ,..., π S ( π 1 + · · · + π S = 1). x The mean (expected value) of thedistribution is the av. value of ther.v.; E [ ] . w w w s ssS = = =∑  µ π  1    Variance of a Distribution x The distribution’s variance is the r.v.’s av.squared deviation from the mean; x Variance measures the r.v.’s variation. var [ ] ( ) . w w w s w ssS = = − =∑ σ µ π  221    Standard Deviation of aDistribution x The distribution’s standard deviationis the square root of its variance; x St. deviation also measures the r.v.’svariability. st. dev [ ] ( ) . w w w w s w ssS = = = − =∑ σ σ µ π  2 21
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