Regarding Statistical Distributions, there are many different types. Among them, the most important one is the Normal (Gaussian) Distribution. The corresponding PDF (Probabilistic Density Function) is given as follows:

Here, indicates Average (mean), and denotes Standard Deviation.

The below Figure shows the Probabilistic Density Function of Normal Distribution, in case that Average is and Standard Deviation is . This example may correspond to the body male height for one population.

As you can see from Figure, the peak of the distribution is around ㎝. Roughly speaking, the width of the hill at the half-height corresponds to the Standard Deviation.

As a check, we can compute the expectation E and Variance V, which give the following results:

and

.

＊We also explain this page in the following video.