Compute DAU and rolling MAU with zero days

You have two tables in PostgreSQL: ### Tables **`users`** - `user_id` (STRING / INT, PK) - `signup_date` (DATE) **`logins`** - `user_id` (STRING / INT, FK → `users.user_id`) - `browser` (TEXT) - `login_ts` (TIMESTAMP) — assume UTC unless stated otherwise ### Tasks 1) **Daily Active Users (DAU)**: For a given date range (e.g., `2023-01-01` to `2023-12-31`), compute DAU where DAU on a day = number of distinct `user_id` that logged in on that calendar day. - Output columns: `date`, `dau` - Requirement: **Include all dates in the range**, even if there were zero logins that day (show `dau = 0`). - Follow-up: If you need a date dimension/calendar, explain how you would create it in PostgreSQL (e.g., via `generate_series`). 2) **Rolling MAU by date**: Compute a **rolling-window MAU** for each calendar date in the range. - Define MAU as **distinct users who logged in in the last 30 days including the current date** (an L30D lookback). - Output columns: `date`, `mau_l30d` - Follow-up discussion: If the product is primarily used on weekdays (little/no weekend usage), what are potential issues with an L30D definition, and what alternative window definitions could be more appropriate?