Everything since Lesson 21 has been about summarizing a posterior — one number, one interval. This lesson asks the posterior to earn its keep: turn it into an actual decision.
Scenario. You built posterior Beta(9, 5) (mean ≈ 0.643) for p — the probability a new
checkout flow outperforms the old one, based on the A/B test data you’ve collected so far. You now
have to decide whether to ship it company-wide.
- If the new flow does outperform (probability
p): shipping earns +$50,000 in additional annual revenue. - If it doesn’t outperform (probability
1 − p): shipping still costs you −$10,000 — cleanup, reverting, the support burden of a flow that turned out to be a net negative.
Expected value of shipping, using your posterior’s mean as your best single estimate of p:
EV(ship) = p × (+$50,000) + (1 − p) × (−$10,000)
Compute the expected value of shipping now, using the posterior mean from Beta(9, 5) as p.
Give your answer in dollars.
(Hold onto this number — the solution will ask a follow-up question the numeric answer alone can’t tell you: given how uncertain this posterior still is, should you actually ship, or run the test a while longer first?)