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#reading-9-probability-concepts

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*).

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**Summary **

o events. According to the total probability rule, if S 1 , S 2 , …, S n are mutually exclusive and exhaustive scenarios or events, then P(A) = P(A | S 1 )P(S 1 ) + P(A | S 2 )P(S 2 ) + … + P(A | S n )P(S n ). <span>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). 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

o events. According to the total probability rule, if S 1 , S 2 , …, S n are mutually exclusive and exhaustive scenarios or events, then P(A) = P(A | S 1 )P(S 1 ) + P(A | S 2 )P(S 2 ) + … + P(A | S n )P(S n ). <span>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). 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

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