Cutting A/B variance in half using yesterday's data
Asked at Microsoft
Your A/B metric (say spend per user) is very noisy because users differ enormously from each other. But you also have each user's spend from the week before the experiment, which is highly correlated with their spend during it.
Explain how CUPED uses that pre-experiment covariate to shrink variance, why it stays unbiased, and how much power you can gain.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.