in terms of a few of moments a probability distribution can often be summarized; the most widely used moments are the mean, or expected value , and the variance.
Note1: mean is the first level moment, variance is the second level(square), the third and fourth level moments are used to study the shape of the probability distribution, in particular, its skewness , S (asymmetry) and kurtosis , K (tallness or flatness).
Note2: when S = 0, a distribution is symmetric; when K equals to 3, it is called mesokurtic (normal distribution), greater than 3 called leptokurtic , less than 3 called platykurtic .