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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

Links

Mathematica statistics web page

See this 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. nma_math502_miner.m

 

2. nma_math502_miner_GUI.m 

 

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

1. nma_math502_monte_carlo.m

 

 

 

 

2. nma_montecarlo_converge.m

monteCarlo_converge

Script to plot Cauchy PDF mean showing it does not converge

nma_cauchy_pdf_mean.m 

cauchy_mean

Table of expected values

 

PDF

HTML 

Mathematica notebook

 

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)

Course projects

First project is here

Second project is here

Population estimation logic flow charts

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

HTML

PDF

image

Chart for estimation of population proportion from a sample

HTML

PDF

image

Chart for estimation of population Variance from a sample

HTML

PDF

image

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

screen_shot

nmaFGM.nb

nmaFGM.nbp

A small note on method of moments, solving using Mathematica

 

 

HTML

PDF

Mathematica notebook