My Mathematics 502 (Probability and Statistics) related material

By Nasser Abbasi

Nov 17,2007

This page will contain collection of statistics related activities I worked on during taking Mathematics 502 at California State Univ. Fullerton in fall 2007. This course is a requirement for the MSc degree in Applied Mathematics and was given by Professor Mortaza (Mori) Jamshidian.

Most of the material is software simulation, some were part of the projects for the course, but most I did on my own.

description

Mathematica statistics web page

Matlab related scripts/functions

 Script description M file Screen shot or output simulate the trapped miner problem (expected time to escape).  (see top of m file for more information)   1. Script without plots   2. This script is same algorithm as above but plots the expected time as simulation is running. 1. Script to simulate monte carlo integration of a function of a single variable on the real line   2. Script to show convergence of monteCarlo integration Script to plot Cauchy PDF mean showing it does not converge

Table of expected values

These tables are generated using Mathematica 6.0

They list the probability density function, the expected value, and the Variance of some common random variables.

Also a table of the expected value of some functions of random variables for different distributions. (The html page does not have lines between rows and columns in the table, this is a problem with Mathematica export, trying to resolve)

I found that making flow charts helps me understand things better. So I started making these for parameters estimation problems.

 Chart name HTML PDF Image Chart for estimation of population mean from a sample Chart for estimation of population proportion from a sample Chart for estimation of population Variance from a sample

Generating bivariate normal distribution

This simulation was written in Mathematica 6.0. This is simulation of the Farlie-Morgenstern method. The input is the mean and variance of 2 random variables (X,Y) which are supposed to be normally distributed. And also an alpha parameter. The output is a the bivariate joint distribution of these above 2 distributions.

 Screen Shot Mathematica 6 notebook Mathematica 6 player formatted notebook

A small note on method of moments, solving using Mathematica