Physical Sciences and Mathematics Commons^™

Multiple Shooting, Monique St-Maurice

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this report was to study the Multiple Shooting method, a numerical method to solve boundary value ordinary differential equation. A FORTRAN program was written to solve the specific problem.

y'' = -y, y(0) = 0, y(π/2) = 1

on a microcomputer, using the microsoft FORTRAN compiler and the 8087 coprocessor.

Monte Carlo Simulation Of The Game Of Twenty-One, Douglas E. Loer

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this paper is to demonstrate the application of computer simulation to the game of Twenty-One to predict a player's expected return from the game. Twenty-One has traditionally been one of the most popular casino games and has attracted much effort to accurately estimate the house's true advantage. Probability theory has been tried, but the thousands of different combinations of cards possible in all hands throughout the entire pack make it practically impossible to apply probability theory without overlooking some possibilities. For this reason, Twenty-One is a perfect candidate for simulation. By blocking several simulations, normal theory can …

Comparison Of Bootstrap And Jacknife Statistical Procedures, Amanuel Gobena

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This report compares the bootstrapping to jacknifing statistical procedures in terms in bias, confidence interval and estimation of median. Related literature have been reviewed. A bootstrap allows a researcher to get an approximation to the distribution of possibly complicated statistical summaries. It is based on random sampling with replacement from experimental units. Jacknife has also been in operation prior to bootstrapping statistical procedure. The jacknife divides the data into subgroups and obtains partial estimates of these subgroups by omitting one subgroup at a time. When both of these statistical resampling procedures are compared the bootstrap has less bias, more accurate …