This question evaluates quantitative estimation, probabilistic modeling, sensitivity analysis, and experiment design skills for a data scientist, including Bayesian uncertainty quantification and funnel conversion accounting.

You are asked to estimate how many users complete registration from a single 30-second Super Bowl TV ad that displays a QR code, then quantify uncertainty, identify key drivers, and outline how to measure incrementality.
Assume independence between steps unless otherwise stated.
(a) Compute the expected number of completed signups.
(b) Provide a 95% credible interval using only the Beta uncertainty on scan propensity (treat all other rates as fixed).
(c) Perform a one-way sensitivity analysis to identify the top three drivers of variance in signups.
(d) Outline a measurement plan to estimate incremental signups (e.g., geo holdout or QR variant holdout) and give a sample-size formula to detect a 5% relative lift with 90% power at α = 0.05, using a baseline signup-per-impression rate derived from the assumptions.
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