the expected value of variable X is the sum over all the products of each value of X times its respective probability.
Note: the expected value seems like a add-weight mean , the probability of each value denotes its individual weight.
eg: X assumes five values: 1, 2, 3, 4, 5; and the probabilities that X assumes these values are 13%, 30%, 26%, 11%, and 20%, respectively. Then the expected value of X is: E(X) = 1x13% + 2x30% + 3x26% + 4x11% + 5x20% = 2.95