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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 sixsided 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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 Spring '11
 AndyRegards

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