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## My Mathematics 504 Simulation Modeling and Analysis, CSU Fullerton

April 23, 2008   Compiled on October 26, 2018 at 8:25am  [public]

### 1 Introduction

This course part of my Masters degree in Applied Mathematics at California State University, Fullerton

Course description (from CSUF catalogue)

MATH 504A Simulation Modeling and: Prerequisites: Math 501A,B; 502A,B; 503A,B. Corequisite: Math 504B. Advanced techniques of simulation modeling, including the design of Monte Carlo, discrete event, and continuous simulations. Topics may include output data analysis, comparing alternative system conﬁgurations, variance-reduction techniques, and experimental design and optimization.Units: (3)

MATH 504B Applications of Simulation Modeling Techniques

Description: Prerequisites: Math 501A,B; 502A,B; 503A,B. Corequisite: Math 504A. Introduction to a modern simulation language, and its application to simulation modeling. Topics will include development of computer models to demonstrate the techniques of simulation modeling, model veriﬁcation, model validation, and methods of error analysis.Units: (3)

#### 1.1 Instructor

Professor Gearhart, W. B. CSUF Math department.

### 2 Handouts given during the course

We followed mostly the instructor class notes pdf

 # date description link 1 Monday 1/22/200 Course description 2 Monday 1/22/08 A problem in conditional probability (the ﬁrst simulation HW, conﬁdence interval, histogram) 3 Monday 1/28/08 Computing project guideline 4 Monday 1/28/08 Continuous approximation to random walks 5 Monday 2/25/08 Problems to practice solving ﬁrst order pde using the characteristics method 6 Monday Craps game and inventory problem. Markov chain computing assignment 7 Monday 3/10/2008 Handout on convergent ﬁnite markov chains 8 Monday 3/17/2008 Key solution to problem 5.7 (HW 8) 9 Monday 3/19/08 Key solution to problem 6.3,6.5 (HW 9) 10 Wed 4/23/20088 Key solution to problem 10.4 to practice on 11 Monday 4/28/2008 Chapter 10 supplement. Kolmogorov equations with worked examples showing how to make the Q matrix 12 Wed 5/7/08 Key solutions to Poisson chapter from lecture notes, chapter 9 13 Wed 5/7/088 Key solutions to continuous time Markov chains, chapter from lecture notes, chapter 10 14 Hastings metropolis algorithm lecture 11

### 3 study notes,lecture notes

Some notes I did during the course HTML

### 4 HWs

 # date description solution code score 1 Wed 2/7/08 Computing Assignment #1 A problem in conditional probability (the ﬁrst simulation HW, conﬁdence interval, histogram) see ﬁrst hand out PDF for more details Matlab source code ﬁle.m 5/5 2 Mon 2/5/08 Derive PDF of Y from an experiment where we switch boxes, uses probability decision tree 2/2 3 Wed 2/20/2008 The long analytical problem. Problem #4 from handout #3 above. Solving Einstein-Weiner pde using fourier transform 2/2 4 Wed 2/27/2008 Computing Assignment #2 The limiting process simulation. Show that random walk ﬁnal position is normally distributed in the limit under the Einstein-Weiner process (see problem 2 in this handout PDF 2/2 5 Wed 2/27/2008 Problem 3.9 from handouts (probability distribution related to record time distribution) 2/2 6 Monday 3/3/2008 Computing Assignment #3 Craps game and inventory problem. Markov chain Problem description is here report Mathematica notebooks code listing HTML 7 Practice problems These are 5 problems to practice using method of characteristics to solve ﬁrst order liner pde. The problems are listed in the handout above. PDF 2/2 8 Monday 3/10/2008 Problem 5.7 from lecture notes (Irreducible matrix, analytical problem) Problem description here Key solution is PDF 2/2 9 Monday 3/17/08 Problems 6.3 and 6.5 from the handout Description here Solution key PDF 2/2 10 Wed 4/16/2008 These problem related to Hastings-Meropolis algorithm. And Prooﬁng a Markov chain is irreducible, regular and time inverse. Implemented the simulation using Mathematica Graded solution. (Entered some data wrong for the numerical problem. corrected) PDF Key solution PDF 8.5 part (a) code Hastings simulation. notebook    PDF 8.5 part(b): direct construction of p matrix from q and $$\pi$$.    notebook    PDF 4/4 11 Wed 5/7/2008 Problems 10.5 and 10.6 These deal with continues time markov chains. To determine rate of arrival and departure for birth/death process 12 Wed 5/7/2008 Computer problem, problem 12.3 in lecture notes. Simulation of problem 10.5 in above HW. Repair shop problem key Matlab code given ﬁle.m Matlab function ﬁle.m 4/4 13 Wed 5/7/2008 Problems 9.3 and 9.5 (On Poisson process) Small Mathematica function for problem 9.5 to plot $$P(X=n)$$ notebook

### 5 Challenge Problems

These are extra problems relating to ﬁrst midterm the instructor gave the class to try to work out. Here are the questions image    image

This is my solution so far HTML