Application of Computerized Monte Carlo Simulation in Evaluating Definite Integrals and Testing of the Properties of Probability Density Functions

Abstract

This work explores a certain application of the Monte Carlo simulation technique in evaluating definite Integrals and x-rays the complexity of solving realistic models by mathematical methods to arrive at an analytic solution. The study has shown that certain complex problems that cannot be solved analytically could be subject to simulations to provide approximate solutions. The work equally studies numerous definite Integrals but provides a result for few through which it is possible to make a generalization in the end of the study. Five probability distributions were highlighted in this work (among others that were investigated) and their properties by Monte Carlo simulation using a PASCAL program where random numbers were generated after numerous trials. Some areas of applications of simulation and the probability distributions studied have been discussed in this study alike.