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"The mean of a discrete random variable Y is defined as: µY = ΣyiPr(Y = yi) where the yi's are the values that the variable takes on and the sum is taken over all possible values. The mean of a random variable is also known as the expected value and is often written as E(Y); that is, E(Y) = µY."
-Statistics for the Life Sciences, 3rd Ed, by Samuels and Witmer
In other words, E here is just your expected value, with E2 being this value multiplied by itself. We were also given a 2nd formula for this which states that E(Y) = µ = Σy * f(y).
An example: Say we are given that in a sample of smoking men, we know that they smoke 1-4 cigarettes per day, and the percentages of this sample that fill each value, as follows (made up, and not statistically accurate):
1 - 20%
2 - 45%
3 - 25%
4 - 10%
Our mean of Y (E) would be: The value in the left column times the value in the right column (in percentage) + the same for each value, as follows: (1 x .2) + (2 x .45) + (3 x .25) + (4 x .1) = 2.25
Source: My college stats textbook, documented above.
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