The total probability rule for expected value states that E(X) = E(X | S1)P(S1) + E(X | S2)P(S2) + … + E(X | Sn)P(Sn), where S1, S2, …, Sn are mutually exclusive and exhaustive scenarios or events.
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Summary
+ P(A | S n )P(S n ). The expected value of a random variable is a probability-weighted average of the possible outcomes of the random variable. For a random variable X, the expected value of X is denoted E(X). <span>The total probability rule for expected value states that E(X) = E(X | S 1 )P(S 1 ) + E(X | S 2 )P(S 2 ) + … + E(X | S n )P(S n ), where S 1 , S 2 , …, S n are mutually exclusive and exhaustive scenarios or events. The variance of a random variable is the expected value (the probability-weighted average) of squared deviations from the random variable’s expected value E(X): σ 2 (X)