$\theta=$ unknown probability that a basketball player makes a shot.

Prior on $\theta$ ~ $Uniform(0,1).$

The player makes two independent shots in a row.

$a.$ What is the posterior density of $\theta?$
$b.$ Estimate the probability of making a third shot.

2. Originally Posted by Anonymous1
$\theta=$ unknown probability that a basketball player makes a shot.

Prior on $\theta$ ~ $Uniform(0,1).$

The player makes two independent shots in a row.

$a.$ What is the posterior density of $\theta?$
$b.$ Estimate the probability of making a third shot.
Start by writting out Bayes' formula for the posterior density of $\theta$.

CB