# Beta Distributions for a Given Mean, Median or Mode

Beta Distributions for a Given Mean, Median or Mode

The beta distribution (x) of a random variable , where and , has mode , mean , median and variance , which are determined by and in a nonintuitive manner. However, once , or has been chosen, can be expressed as a function of its value and becomes the sole determinant of the distribution's spread. This Demonstration calculates and plots the beta distribution's probability density function (PDF) and cumulative distribution function (CDF) for chosen values of the mode, mean or median and displays the numerical values of all three, as well as the corresponding variance.

f

α,β

x

0≤x≤1

α,β⩾1

x

mode

x

mean

x

median

2

σ

α

β

x

mode

x

mean

x

median

β

α