The different faces of the
Beta distribution
Parameter choices for α and β and corresponding
density bounded between 0 and 11
α β
equal alpha and beta
0.5 0.5
1 1
2 2
8 8
smaller alpha
0.5 1
1 2
1 8
2 8
smaller beta
1 0.5
2 1
8 1
8 2

1 f(x;α,β)=B(α,β)-1xα (1-x)β,
where the Beta function B is a normalizing constant
to ensure that the total probability is 1.