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Beta Distributions for a Given Mean, Median or Mode

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plot paramater
mode
mean
median
mode
FE`userMode$$8370446560649006078357750477513218012226
mean
FE`userMean$$8370446560649006078357750477513218012226
median
FE`userMedian$$8370446560649006078357750477513218012226
α
FE`\:03b1$$8370446560649006078357750477513218012226
f
max
FE`fMax$$8370446560649006078357750477513218012226
restore initial settings
The beta distribution
f
α,β
(x)
of a random variable
x
, where
0≤x≤1
and
α,β⩾1
, has mode
x
mode
, mean
x
mean
, median
x
median
and variance
2
σ
, which are determined by
α
and
β
in a nonintuitive manner. However, once
x
mode
,
x
mean
or
x
median
has been chosen,
β
can be expressed as a function of its value and
α
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.
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