Data Science Assignment: Monte Carlo Simulation Problems and Solutions

This assignment solution delves into the application of Monte Carlo simulations, a powerful computational technique used for risk assessment and decision-making, particularly in scenarios with uncertain variables. The solution addresses multiple problems, starting with an integration problem solved using both theoretical and coded approaches in R. It then explores cumulative distribution function (CDF) plots, illustrating how they visualize the distribution of data, and includes examples using normal distributions. The assignment further covers various sampling techniques, including rejection sampling and squeezed rejection sampling, which are crucial for generating random numbers from complex distributions. The student demonstrates the use of these techniques through code and analysis, providing insights into the advantages and considerations of each method. The solution also includes the use of statistical concepts such as variance and the generation of random variables. The assignment concludes with a discussion of the squeezed rejection sampling method, highlighting its advantages over standard rejection sampling, and providing a practical example.