Schema and sample data (PostgreSQL): users(id, signup_date, country) 1 | 2025-08-20 | US 2 | 2025-08-25 | US 3 | 2025-08-27 | CA 4 | 2025-08-30 | US 5 | 2025-08-31 | IN events(user_id, event_date, event_type, revenue) 1 | 2025-08-21 | visit | 0 1 | 2025-08-26 | purchase | 50 2 | 2025-08-26 | visit | 0 2 | 2025-09-01 | purchase | 20 3 | 2025-08-28 | visit | 0 3 | 2025-08-31 | purchase | 30 4 | 2025-08-31 | visit | 0 5 | 2025-09-01 | visit | 0 Tasks (use window functions where appropriate; treat "today" as 2025-09-01): (a) Compute, by country, the 7-day conversion rate on 2025-09-01, defined as users with ≥1 purchase in [2025-08-26, 2025-09-01] divided by users with ≥1 visit in the same window (users must have signed up by 2025-09-01). Ensure each user counts at most once in numerator and denominator. (b) For each user, return first_purchase_date and days_to_convert from signup_date; use window functions to de-duplicate events. (c) Using a self join, list users who had at least one visit strictly before their first purchase. (d) Explain when LEFT JOIN vs RIGHT JOIN changes results in (a) if some countries have no purchases during the window.