Best Gemini prompts for Mathematicians

I have a regression model that predicts customer churn based on demographic and behavioral data, with coefficients of 0.5 for age, 0.2 for income, and 0.1 for purchase history. Using a dataset of 10,000 customers, with 20% churn rate, and assuming a normal distribution of residuals, validate the model's performance using metrics such as mean squared error, R-squared, and cross-validation, and provide a detailed report on the model's strengths and weaknesses, including any potential issues with multicollinearity, heteroscedasticity, or non-linearity.

Design an optimized ETL pipeline for a dataset of 100 million records, with 50 columns, and a data size of 10 GB, using Snowflake as the data warehouse, Python as the scripting language, and Tableau for data visualization, assuming a daily data ingestion schedule, and provide a detailed report on the pipeline's performance, including metrics such as data processing time, memory usage, and data quality, and identify potential bottlenecks and areas for improvement, such as data partitioning, parallel processing, or data caching.

Generate a comprehensive statistical summary for a dataset of exam scores, with 1,000 students, 5 subjects, and a total of 5,000 records, including metrics such as mean, median, mode, standard deviation, variance, and correlation coefficients, and provide a detailed report on the distribution of scores, including any potential outliers, skewness, or kurtosis, and visualize the results using histograms, box plots, and scatter plots, and assume a normal distribution of scores, with a mean of 70 and a standard deviation of 10.

Assess the data quality of a dataset of customer information, with 500,000 records, 20 columns, and a data size of 1 GB, using metrics such as data completeness, data consistency, data accuracy, and data timeliness, and provide a detailed report on the data quality issues, including any potential problems with missing values, duplicate records, or data formatting, and identify potential root causes and recommend solutions, such as data validation, data normalization, or data standardization, and assume a data quality threshold of 95% for completeness and accuracy.