| # Sample and weighted average, expected value The sample average of given numbers , is defined as The sample average can be interpreted as a scalar product: where is the vector containing the samples, and , with the vector of ones. More generally, for any vector , with for every , and , we can define the corresponding weighted average as . The interpretation of is in terms of a discrete probability distribution of a random variable , which takes the value with probability , . The weighted average is then simply the expected value (or, mean) of under the probability distribution . The expected value is often denoted , or if the distribution is clear from context.