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Compute and Interpret UCB1 Scores
Three ad creatives have accumulated the following data after t = 1{,}000 total impressions across all three:
| Creative | Clicks | Impressions |
|---|---|---|
| X | 40 | 500 |
| Y | 15 | 100 |
| Z | 90 | 400 |
- Compute the empirical click-through rate and the UCB1 score for each creative.
- Which creative does UCB1 select next, and is this the creative with the highest empirical CTR? Explain why or why not.
- Suppose Y's impression count triples to 300 with the same 15% empirical CTR (45 clicks). Recompute Y's UCB1 score and explain qualitatively what changed and why.
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