San Francisco State University
Department of Mathematics
Course Syllabus
MATH 324
Probability and Statistics with Computing
Prerequisites
A grade of C or better in MATH 227 (Calculus II) and some computer
programming experience.
Bulletin Description
Basic concepts of probability and statistics. Data analysis, probability
distributions, confidence intervals, and hypothesis testing.
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
•
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 weeks)
•
Probability Theory: Axioms of Probability, Combinatorics, General
Probability Rules , Some elementary Theorems, Conditional Probability,
Independent Events, Bayes’s Theorem (3 weeks)
•
Probability Distributions: Random Variables, Discrete Probability
Distributions, Continuous Probability Densities, Normal approximation
to Binomial, Mean, Variance, Chebyshev’s Theorem (4 weeks)
•
Probability and Sampling Distributions: Law of Large Numbers, Central
Limit Theorem, t-distribution, Chi-Square distribution(2 weeks)
•
Estimation: Point Estimation, Margin of Error, Confidence Interval
Estimation for means, proportions, and variances for one and two sample
problems (2 weeks)
•
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
weeks
Textbooks and Software
Recent text books include:
Probability and Statistics for Engineers and the Sciences, Jay L. Devore,
Brooks/Cole
Miller & Freund’s Probability and Statistics for Engineers, Richard A. Johnson,
Prentice Hall
Programming with high level languages and/or statistical packages
Submitted by: M. R. Kafai
Date: June, 18, 2003