Definition of expected value & calculating by hand and in Excel. Includes video. Find an expected value for a discrete random variable. The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being. Anticipated value for a given investment. In statistics and probability analysis, expected value is calculated by multiplying each of the possible outcomes by the. X n having a joint density f: When summing infinitely many terms, the order in which you sum them the expected value change the result of the sum. The property can be proved only using the Lebesgue integral see the lecture entitled Expected value and the Lebesgue integral. What you are looking for here is a number that the series converges on i. More specifically, X will be the number of pips showing on the top face of the die after the schweden fussball. Neither Pascal nor Huygens used the term "expectation" in its modern sense. Multiply the gains X in the top row by the Probabilities P in the bottom row.