Beta Distribution

This is a continuous distribution.
We can use this distribution when we know how many outcomes succeeded and how many failed (but we don't know the probability of success).
This is bounded between 0 and 1
Beta is a two-variable function
The relation between beta and gamma function will help to solve many problems in physics and mathematics
The most widely used has 2 parameters and is a family of distributions
The PDF is not just flat

Example - Throwing a Coin

We have been given a coin but we want to check that the coin is fair.
If the coin is equally weighted then there will be a 50% probability of getting a Head and a 50% probability of getting a Tail.
If one side of the coin is slightly heavier that the other, the probabilities might not be the same.

We are going to throw our coin 100 times and record the results.
65 Heads and 35 Tails.

BETA.DIST -
This models the probability of a probability - this is a flexible family and has lots of nice connections to other distributions

BETA.INV -
This is often used as a prior for a parameter that is a probability (between 0 and 1)

Note the following equality when s and n are positive integers with n > s: BETA.DIST(p, s, n-s, TRUE) = 1 - BINOM.DIST(s-1, n-1, p, TRUE)

What is the 95% confidence interval?
We can use cumulative = true

Properties

Assumptions