Write SQL for DAU and first-purchase conversion

Today is 2025-09-01. Using the schema and sample data below, write a single ANSI-SQL query that returns one row per day for the last 7 days (2025-08-26 to 2025-09-01 inclusive) with columns: day (DATE), dau (distinct users with a 'session' event that day), new_buyers (users whose first-ever order occurs that day), and conv_rate (new_buyers/dau rounded to 2 decimals; return 0.00 when dau=0). Rules: count only event_type='session' for DAU; a user's 'first-ever' order is the minimum order_date across all their orders; include dates with zero activity. Schema: users(user_id INT PRIMARY KEY, signup_date DATE); events(user_id INT, event_date DATE, event_type VARCHAR); orders(order_id INT PRIMARY KEY, user_id INT, order_date DATE, amount DECIMAL(10,2)). Sample tables: users +---------+-------------+ | user_id | signup_date | +---------+-------------+ | 1 | 2025-08-15 | | 2 | 2025-08-30 | | 3 | 2025-09-01 | | 4 | 2025-08-10 | +---------+-------------+ events +---------+------------+------------+ | user_id | event_date | event_type | +---------+------------+------------+ | 1 | 2025-08-26 | session | | 1 | 2025-08-27 | session | | 1 | 2025-09-01 | session | | 2 | 2025-08-31 | session | | 2 | 2025-09-01 | session | | 3 | 2025-09-01 | session | | 4 | 2025-08-26 | session | | 4 | 2025-08-26 | click | | 4 | 2025-08-27 | session | +---------+------------+------------+ orders +----------+---------+------------+--------+ | order_id | user_id | order_date | amount | +----------+---------+------------+--------+ | 101 | 1 | 2025-08-27 | 50.00 | | 102 | 2 | 2025-09-01 | 20.00 | | 103 | 4 | 2025-08-26 | 15.00 | | 104 | 1 | 2025-09-01 | 25.00 | +----------+---------+------------+--------+