Best ChatGPT prompts for Mathematicians

Given a dataset of 10,000 samples with 20 features, and a regression model that achieves a mean squared error of 0.05, validate the model's performance by generating 1000 synthetic datasets with similar statistical properties, and calculate the average mean squared error and R-squared value across these datasets, considering the effects of feature correlation and noise on model robustness.

Design an optimized ETL pipeline for a Snowflake database that ingests 100 GB of JSON data daily, with 50% of the data requiring data cleansing and transformation, and the remaining 50% requiring aggregation and filtering, using Python and the Snowflake SQL API, and provide a step-by-step breakdown of the pipeline's components, including data ingestion, processing, and loading, as well as estimated execution times and resource utilization.

Generate a comprehensive statistical summary for a dataset of exam scores, including measures of central tendency, dispersion, and correlation, as well as visualizations of the data distribution and relationships between variables, using Python and the Tableau API, and provide a detailed interpretation of the results, highlighting any notable trends, patterns, or outliers, and discussing potential implications for educational policy and decision-making.

Given a data warehouse with 100 million rows and 10 tables, optimize a complex SQL query that joins 5 tables, applies 3 filters, and aggregates data using 2 group-by clauses, by analyzing the query execution plan, identifying performance bottlenecks, and recommending indexing strategies, data partitioning schemes, and optimization techniques to reduce query execution time by at least 30%, and provide a step-by-step guide to implementing these optimizations and verifying their effectiveness.