Course Title：Probability & Statistics
Course Code：12793
Number of Credits: 3
Teaching Hours: 48
Prerequisites: Calculus I, Calculus II
Overview
The use of probability models and statistical methods for analyzing data has become common practice in virtually all scientific disciplined. This course attempts to provide a comprehensive introduction to those models and methods most likely to be encountered and used by students in their careers in engineering and the natural sciences. Although the examples and exercises have been designed with scientists and engineers in mind, most of the methods covered are basic statistical analyses in many other disciplines, so that students of business and the social sciences will also profit from studying this course.
Students in a statistics course designed to serve other majors may be initially skeptical of the value and relevance of the subject matter. Experience provides that students can be turned on to statistics by the use of good examples and exercises that blend their everyday experiences with their scientific interests. Many of the methods presented, especially in the later chapters on statistical inference , are illustrated by analyzing data taken from a published source and many of the exercises also involve working with such data.
Syllabus
Chapter 1 Overview and Descriptive Statistics
Introduction
1.1 Populations, Samples, and Processes
1.2 Pictorial and Tabular Methods in Descriptive Statistics
1.3 Measures of Location
1.4 Measures of Variability
Supplementary Exercises
Bibliography
Chapter 2 Probability
Introduction
2.1 Sample Spaces and Events
2.2 Axioms, Interpretations and Properties of Probability
2.3 Counting Techniques
2.4 Conditional probability
2.5 Independence
Supplementary Exercises
Bibliography
Chapter 3 Discrete Random Variables and Probability Distributions
Introduction
3.1 Random Variables
3.2 Probability Distributions for Discrete Random Variables
3.3 Expected Values of Discrete Random Variables
3.4 The Binomial Probability Distribution
3.6 The Poisson Probability Distribution
Supplementary Exercises
Bibliography
Chapter 4 Continuous Random Variables and Probability Distributions
Introduction
4.1 Continuous random variables and probability density functions
4.2 Cumulative Distribution Functions and Expected Values
4.3 The Normal Distribution
Supplementary Exercises
Bibliography
Chapter 5 Joint Probability Distributions and Random Samples
Introduction
5.1 Jointly Distributed Random Variables
5.2 Expected Values, Covariance, and Correlation
5.3 Statistics and their Distributions
5.4 The Distribution of the Sample Mean
5.5 The Distribution of a Linear Combination
Supplementary Exercises
Bibliography
Chapter 6 Point Estimation
Introduction
6.1 Some General Concepts of Point Estimation
6.2 methods of point estimation
Supplementary Exercises
Bibliography
Chapter 7 Statistical Intervals Based on a Singles Sample
Introduction
7.1 Basic properties of confidence intervals
7.2 Large-sample confidence intervals for a population mean and proportion
7.3 Intervals based on a normal population distribution
7.4 Confidence intervals for the variance and standard deviation of a normal population
Supplementary Exercises
Bibliography
Chapter 8 Testing of Hypotheses based on a single sample
Introduction
8.1 Hypotheses and test procedures
8.2 Tests about a population mean
8.3 Tests concerning a population proportion
8.4 P-values
8.5 Some comments on selecting a test procedure
Supplementary Exercises
Bibliography
Chapter 12 Simple Linear Regression and Correlation
Introduction
12.1 The Simple Linear Regression model
12.2 Estimating model parameters
12.3 Inferences about the slope parameter
Supplementary Exercises
Bibliography
Assessment
Form of assessment Weighting
Assignment 40%
Exam 60%
Teacher’s information
Sheng Jiliang
Tao Changqi
Liu Manfeng
Mao Xiaobing
Textbook
Probability and statistics for engineering and the sciences (fifth edition)
Jay L.Devore California Polytechnic State University