# MATH 324: Probability and Statistics with Computing

Prerequisites & Bulletin Description

## Course Objectives

This course provides a thorough background in the mathematics of probability and statistics including the use of standard statistical computer packages such as SAS, SPSS, MINITAB and/or some computer programming. It covers basic combinatorics, descriptive statistics including graphical treatments and numerical summaries of data, the axioms and theorems of probability theory, discrete and continuous probability functions and inferential statistics including estimation and hypothesis tests for one- and two- sample problems. This course is primarily designed for Computer Science and engineering majors. The students will learn to do data presentation with tables, graphs and calculation such as mean, media, standard deviation. They will be able to use probability and distribution theory for many of their applications in various fields of science in particular in Computer Science and Engineering. The teaching of estimation and testing will enable the students to analyze data and make correct statistical conclusion.

## Evaluation of Students

Instructors' assessment is usually based on homework, quizzes, computer assignments, in-class exams and an in-class final.

## Course Outline

Topics & Length
Topics Number of Weeks
Introduction: Some examples where statistics is applicable; Need for mathematical models
Descriptive Statistics: Frequency tables, Histograms, Bar graphs, Pie charts, Stem-and-Leaf plots, Time plots, Boxplots, and their interpretation; Measures of central tendency (Mean, Median, Mode); Measures of dispersion (Range, Percentiles, Interquartile range, Variance, Standard Deviation) 1
Probability Theory: Axioms of Probability, Combinatorics, General Probability Rules , Some elementary Theorems, Conditional Probability, Independent Events, Bayes's Theorem 3
Probability Distributions: Random Variables, Discrete Probability Distributions, Continuous Probability Densities, Normal approximation to Binomial, Mean, Variance, Chebyshev's Theorem 4
Probability and Sampling Distributions: Law of Large Numbers, Central Limit Theorem, t-distribution, Chi-Square distribution 2
Estimation: Point Estimation, Margin of Error, Confidence Interval Estimation for means, proportions, and variances for one and two sample problems 2
Test of Significance: Null and Alternative Hypotheses, Type I and Type II Errors, Significance Level, p-value, Hypothesis testing for means, variances, and proportions for One-Sample and Two-Sample problems. 2

## Textbooks & Software

Jay L. Devore, Probability and Statistics for Engineers and the Sciences, Brooks/Cole

Richard A. Johnson, Miller & Freund's Probability and Statistics for Engineers, Prentice Hall

Programming with high level languages and /or statistical packages

Submitted by: M. R. Kafai
Date: June 18, 2003