Design and implement a distributed and parallel database system using PostgreSQL for an ecommerce pla:orm. Focus on the following requirements: $1.$ Brief the requirements for the database system and the assumpCons considered for the system. Provide an EnCty RelaCon Diagram for the system and show the transformaCon of the ER diagram. $2.$ Create a PostgreSQL database schema for the pla:orm with the required tables. Ensure that the schema is normalized and opCmized for effecCve querying. $3.$ Implement fragmentaCon strategies on the system. Select any table from the defined schema for fragmentaCon and implement an appropriate type of fragmentaCon, i$.$e$.,$ horizontal, verCcal, or hybrid, based on the characterisCcs of the chosen table. Consider the impact of fragmentaCon on query performance and propose opCmizaCon techniques. Provide SQL commands or scripts to implement the chosen fragmentaCon strategy. $4.$ Implement a strategy for handling concurrent transacCons. Implement a sample transacCon for order placement and payment, ensuring data consistency in a parallel execuCon environment. $5.$ Implement access controls using PostgreSQL's role$-$based authenCcaCon. Define roles for customers, administrators, and a superuser with appropriate permissions. $6.$ Design and implement a data replicaCon strategy for fault tolerance. Replicate customer data across nodes and show how the system deals with node failures. $7.$ Write and execute opCmized SQL queries for e$-$commerce operaCons, like retrieving product details, customer orders, and payment history. UClize parallel query execuCon wherever applicable. $8.$ Implement a sample transacCon involving mulCple SQL statements including error handling. Also, demonstrate the use of transacCons and rollbacks in the distributed environment provide all the answers and queries for all the questions