Evaluate and prioritize Facebook Groups

Answer all parts concisely, with formulas and concrete decision rules. 1) Measure success: Propose a KPI hierarchy for Facebook Groups covering member value, creator value, and platform health. Provide exact metric definitions (e.g., weekly commenter rate, median time-to-first-reply, churn hazard) and guardrails (e.g., cross-surface cannibalization: News Feed views per DAU). 2) Resource prioritization: You can improve either small groups (<100 monthly active members) or large groups (≥1000). Build a prioritization framework using marginal ROI: define an incremental value per engineering week that combines uplift to retention and quality-adjusted interactions. Show how you would estimate diminishing returns and uncertainty, then choose which segment to fund under a fixed quarterly budget. 3) Observation: Posts in Groups receive more comments than posts from friends/business accounts. List at least three plausible causal mechanisms and three confounders. Design a verification plan that distinguishes causality from selection: include stratified matching by author and audience size, within-user cross-surface randomized holdouts (if available), and a DID that exploits group join dates. Specify the exact regression you would run, including fixed effects and key interaction terms, and how you would validate common-trends. 4) Decision: Given mixed evidence (Groups +8% comments but −2% reach on Feed), state the product decision you would recommend, the thresholds under which you would reverse it, and what additional logging you require to monitor long-term community health.