Expected values

Printer-friendly versionPrinter-friendly version Expected Value (i.e., Mean) of a Discrete Random Variable Law of Large Numbers: Given a large number of repeated trials, the average of the results will be approximately equal to the expected value

Expected value: The mean value in the long run for many repeated samples, symbolized as E(X)E(X) Expected Value for a Discrete Random Variable

E(X)=∑xipi E(X)=∑xipi xixi= value of the ith outcome pipi = probability of the ith outcome

According to this formula, we take each observed X value and multiply it by its respective probability. We then add these products to reach our expected value. You may have seen this before referred to as a weighted average. It is known as a weighted average because it takes into account the probability of each outcome and weighs it accordingly. This is in contrast to an unweighted average which would not take into account the probability of each outcome and weigh each possibility equally.