Posterior Mean of a Beta Distribution

Statistics

Bayesian Inference

Easy

Using the posterior

Beta (7, 8)

, what is the posterior mean?

Hint 1

The mean of a $Beta (α, β)$ distribution has a standard closed form.

Hint 2

Substitute the given parameters into that formula.

Show worked solution

1. Apply the Beta mean formula
The mean of $Beta (α, β)$ is $\frac{α}{α + β}$ .
2. Substitute values
With $α = 7$ and $β = 8$ :
$E [p] = \frac{7}{7 + 8} = \frac{7}{15}$

Answer: 7/15

1. Apply the Beta mean formula