Estimate Super Bowl QR-driven registrations

Estimate the number of completed registrations from a Super Bowl QR-code ad. Assumptions: 115,000,000 unique TV viewers; QR visible for 30 seconds in a single 30s spot; device-available rate among viewers = 82%; per-viewer scan propensity ~ Beta(12, 780) (mean ≈ 1.51%); 12% of scans are duplicate attempts from the same person; 4% of scans are bot/invalid; landing infrastructure drops 6% of requests at peak; among valid, unique sessions that reach the landing page, 68% click “Start sign up”; form completion (without incentive) = 72%; SMS 2FA delivery success = 94%; among delivered, 3% fail verification; the $15 coupon increases form completion odds by 25% multiplicatively (odds ratio = 1.25). Tasks: (a) Compute the expected number of completed signups; (b) Provide a 95% credible interval using only the Beta uncertainty on scan propensity while treating other rates as fixed; (c) Perform a one-way sensitivity analysis to identify the top three drivers of variance in signups; (d) Briefly outline a measurement plan to estimate incremental signups (e.g., geo holdout or QR variant holdout) and specify a sample-size formula to detect a 5% relative lift with 90% power at α=0.05 given a baseline signup-per-impression rate you derive from the assumptions.