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Contents Probability and Expected Value Expected value Linear combination of expected values Probability and Expected Value A quantitative indicator for mathematically describing the characteristics and shape of random variables and probability distributions is called moment . $$\begin{aligned}&\text{nth order moment }= E(x^n)\\ &n= 1, 2, \cdots \end{aligned}$$ Moments are used to derive various statistics such as skewness and kurtosis along with mean and variance introduced in descriptive statistics. Expected value The mean is the most commonly used statistic to characterize variables. This statistic is calculated as the product of the frequency and probability for each variable value and is called expected value (E(X)). Each value of the random variable X can be specified by the relative likelihood, that is, the probability function, which is the probability that the value can appear compared to other values. When the v...