You are given two tables that track signups and user transactions. ## Tables ### `users` - `user_id` (STRING, **PK**) — unique user - `signup_ts` (TIMESTAMP) — time the user signed up (assume UTC) ### `transactions` - `transaction_id` (STRING, **PK**) - `user_id` (STRING, **FK → users.user_id**) - `transaction_ts` (TIMESTAMP) — time of transaction (UTC) - `amount` (NUMERIC) — transaction amount ## Task You want an **early signal** that predicts **Day-30 retention**. 1) Define an **early engagement metric** as the number of transactions a user makes in the first **7 days after signup**: - `early_txn_cnt` = count of `transactions` where `transaction_ts >= signup_ts` and `transaction_ts < signup_ts + 7 days`. 2) Define **Day-30 retention** as whether the user has **at least one transaction** in the window **[signup + 30 days, signup + 37 days)**. - `is_retained_d30` ∈ {0,1} 3) Write a SQL query that outputs retention performance by early-engagement bucket: - Bucket `early_txn_cnt` into: `0`, `1`, `2`, `3+` ## Required output Return one row per bucket with: - `early_txn_bucket` - `users_in_bucket` - `retained_users` - `retention_rate` (= `retained_users` / `users_in_bucket`, as a decimal) ## Notes / assumptions - Include users with zero transactions. - If a user has transactions before `signup_ts`, ignore them. - If multiple transactions occur in the retention window, the user still counts as retained once.