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The concept of moment in Mathematics evolved from the concept of ''' Moment ''' in Physics . The ''n''th moment of a real-valued function ''f''(''x'') of a real variable about a value ''c'' is : The moments about zero are usually referred to simply as the moments of a function. Usually, except in the special context of the problem of moments Below , the function will be a Probability Density Function . The moments (about zero) of a probability density function ''f''(''x'') are the Expected Value s of ''X''''n'', the moments about its mean μ are called ''central'' Moments ; These describe the shape of the function, independently of Translation . If (lower-case) ''f'' is a Probability Density Function , then the value integral above is called the ''n''th moment of the Probability Distribution . More generally, if (capital) ''F'' is a Cumulative Probability Distribution Function of any probability distribution, which may not have a density function, then the ''n''th moment of the probability distribution is given by the Riemann-Stieltjes Integral : where ''X'' is a Random Variable that has this distribution. When |
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