Define and critique a user activity metric

Context

You are on a product team and need to define a metric for user activity to be used in dashboards and decision-making.

Question

1. Propose 2–4 candidate definitions of “active user” (e.g., DAU/WAU/MAU), including the exact event logic (what counts as activity).
2. For each definition, discuss:
   • pros/cons and what product behavior it captures
   • sensitivity to spam/bots, accidental opens, and background activity
   • how it behaves with different product usage patterns (daily vs occasional)
   • how time windowing/timezone choices affect the metric
3. Recommend a primary metric plus diagnostic and guardrail metrics you would pair with it, and explain why.

Assume you have event logs with at least: user_id, event_name, event_time (UTC), platform, and relevant event properties.