# Beta Distribution

Let $X∼Beta(α,β)$., then the PDF of Beta Distribution is given by $f(x)=Γ(α)Γ(β)Γ(α+β) x_{α−1}(1−x)_{β−1},for0≤x≤1$

$α$ and $β$ will determine the shape of the distribution. Conceptually,

- $α$ represents number of successes
- $β$ represents number of failures

Cool Visualization

Expectation and variance:

- $E(X)=a+ba $
- $Var(X)=(a+b)_{2}(a+b+1)ab $

As you increase $α$ and $β$, the graph becomes spikier, which results more confidence in the mean.