Beta Distribution Conjugacy
2 points possible (graded)
In this problem, we will explore the use of the Beta distribution family in Bayesian statistics. This family of distributions is especially suited for the Bayesian framework because it covers a large variety of distribution shapes, only uses two parameters, and simplifies computation as updates may be done by simple addition to the parameters.
For this particular problem, our parameter of interest is \( p \). Our prior distribution is Beta \( (a, b) \), and conditional on \( p \), we have observations \( X_{1}, X_{2}, \cdots X_{n} \stackrel{\text { i.i.d }}{\sim} \operatorname{Ber}(p) \). As discussed in lecture, the posterior distribution is also a Beta distribution Beta \( (\alpha, \beta) \). What are its parameters \( \alpha \) and \( \beta \) ?
Use SumXi for \( \sum_{i=1}^{n} X_{i} \).
\[
\alpha=
\]
\( \square \)
\[
\beta=
\]
\( \square \)