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    IBMediumStatistics10–12

    Mean and Variance of a Discrete Distribution

    Média e Variância de uma Distribuição Discreta

    A discrete random variable XX takes the values 00, 11, 22, 33 with probabilities 0.10.1, 0.30.3, 0.40.4, 0.20.2 respectively. Find E(X)\mathrm{E}(X) and Var(X)\mathrm{Var}(X).

    The mean weights each value by its probability. For the variance, the shortcut formula needs a second weighted sum — and it is the squares of the values that are weighted, not the mean.

    Solution

    Step 1 of 9

    1. 1.Check the probabilities sum to one: