差分

Given a dataset of a sample <math>X = derived from a population, of which observed values and distribution ( x_1e.g.,\ x_2normal distribution,\ x_3binary distribution,\ \cdots logistic distribution, etc.)</math> derived from a populationare known, its parameters (e.g., the sample mean <math>\bar{X}</math> and the sample standard deviation <math>s</math> , success probability and number of trials, location and scale, etc. ) can be calculatedobtained.

Chance that a value in <math>Xx_i</math> in the sample is in a range of certain values like (e.g., <math>x_i > n</math> ) can also be calculated from the dataset. This chance is <math>probability</math>.

:<math>probability = P(x_i>n\text{ in a range}|\bartext{Xparameters},s)</math> For example, if a dice was rolled 600 times and numbers of 1 to 6 appeared 100 times for each, the mean is 3.5 and the standard deviation is 1.71. Probability that a value is 1 in that sample is, :<math>probability = P(x_i=1|3.5,1.71) = 100/600 = 1/6 </math>