Set the Group Call participant cap
Overview
This question evaluates a candidate's competency in applied statistical modeling, change‑point or segmented regression, uncertainty quantification, sample‑size estimation and robustness analysis using telemetry to set operational participant caps while meeting QoE guardrails such as median MOS and dropped‑call rate.
We must set a maximum participants cap K for Group Calls. You have telemetry at the call level: calls(call_id, start_ts, participants_count, video_on_ratio, median_mos_score, p95_jitter_ms, packet_loss_pct, bitrate_kbps, cpu_load_pct, network_type, region, device_tier, dropped_call_flag). Propose a statistical method to choose K that maximizes total successful participant‑minutes subject to guardrails: P95 median_mos_score ≥ 3.8 and dropped_call_rate ≤ 2%. Include: (a) how you’d fit and validate a piecewise/segmented regression or change‑point model of QoE vs participants_count; (b) how you’d compute uncertainty on K and report a 95% CI that is within ±1 participant; (c) whether to output a single global K or dynamic caps by device/network, and the decision rule to collapse to a single product limit; (d) how much data (number of calls) you need to estimate K with the required precision and how you’d check robustness to heavy‑tail outliers.