notes 19

# notes 19 - Mean also called Expected Value of a Discrete...

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Mean, also called Expected Value, of a Discrete Variable Submitted by gfj100 on Wed, 11/11/2009 - 10:40 The phrase expected value is a synonym for mean value in the long run (meaning for many repeats or a large sample size). For a discrete random variable, the calculation is Sum of (value× probability) where we sum over all values (after separately calculating value× probability for each value), expressed as: E(X) = , meaning we take each observed X value and multiply it by its respective probability. We then add these products to reach our expected value labeled E(X). [NOTE: the letter X is a common symbol used to represent a random variable. Any letter can be used.] Example : A fair six-sided die is tossed. You win \$2 if the result is a “1”, you win \$1 if the result is a “6” but otherwise you lose \$1. The probability distribution for X = amount won or lost is X +2 +1 -1 Probability 1/6 1/6 4/6 Expected Value = (2 × ) + (1 × ) + (-1× ) = -1/6 = -\$0.17. The interpretation is that if you play many times, the average outcome is losing 17 cents per

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notes 19 - Mean also called Expected Value of a Discrete...

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