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#reading-9-probability-concepts

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.

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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)

+ 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)

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