Estimate billboard reach and impressions

A single digital billboard sits beside a 6-lane urban expressway. You must estimate weekly unique reach (people who saw it at least once) and total impressions, and then extend to estimate conversion to store visits using a simple Markov chain model. Given data and assumptions: - Average weekday vehicles/day: 80,000; weekend: 50,000. Average occupants/vehicle: 1.4. - Visibility probability per pass depends on lane and time: p_vis = 0.75 (daytime), 0.55 (night), weighted by 70% daytime traffic. - Share of traffic by segment: locals living within 3 km (30%), commuters passing ≥4 weekdays (50%), occasional passers (20%). - For commuters, passes/week ~ Poisson(λ=5). For locals, passes/week ~ Poisson(λ=2). For occasional, passes/week ~ Poisson(λ=1). - Deduplicate unique people using mobile location panel of 120,000 devices/week within 500 m; device-to-person expansion factor: 2.2; panel capture rate uncertainty ±10% (1σ). Tasks: 1) Estimate weekly unique reach and total impressions with 95% CIs, clearly stating all formulas and independence assumptions. Show how you combine traffic counts, occupancy, visibility, and pass frequency to compute impressions, and how you deduplicate to people-level using the panel (include the capture-rate uncertainty via delta method or bootstrap). 2) Using a 3-state Markov chain (Unaware → Aware → Visit), propose reasonable transition probabilities by segment and compute expected visits/week attributable to the billboard. Discuss sensitivity of results to these probabilities and to p_vis. 3) Identify at least three major bias sources (e.g., panel selection, deduplication error, dwell-time bias) and propose corrections/validations.