# Beta Distribution
The **Beta Distribution** can be thought of [as a distribution over things that can be probabilities](https://youtu.be/CEVELIz4WXM?t=401) (this is also mentioned in chapter 7 of Bayesian Methods for Hackers, pg 195). The Beta Distribution specific deals with scenarios in which we are only dealing with *two things*. For instance, the probability of observing a heads or a tails. Let us define the following:
$p_h = \text{probability of heads}$
$p_t = \text{probability of tails}$
With a *constraint*:
$p_h + p_t = 1$
This allows us to effectively only need to model one of the probabilities, since the constraint allows us to determine the other.
### Density Function
The Beta Distribution has the following probability density function:
$
f(x; \alpha, \beta) =
\frac{ x^{\alpha - 1} (1-x)^{\beta - 1} }
{B(\alpha, \beta)}
$
Where $B$ is the **Beta Function**:
$B(x, y) = \int_0^1 t^{x - 1} (1 - t)^{y - 1}dt$
### Visual
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Date: 20220510
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What distribution should be used when trying to model the probability parameter, $p$, of a **bernoulli distribution**?
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