AMS 310, Survey of Probability and Statistics

Catalog Description: A survey of data analysis, probability theory, and statistics. Stem and leaf displays, box plots, schematic plots, fitting straight line relationships, discrete and continuous probability distributions, conditional distributions, binomial distribution, normal and t distributions, confidence intervals, and significance tests. May not be taken for credit in addition to ECO 320.  SBC: STEM+

Prerequisite: AMS 161 or MAT 127 or MAT 132

3 credits

Course Materials:

SPECIAL NOTE:  EACH INSTRUCTOR HAS HIS/HER OWN LINK FOR THE COURSE MATERIALS.  Please be certain you choose the correct link when ordering your materials.  If the instructor has more than one section, be sure to choose the section you enrolled in for the Active Learning selection.

 

SPRING 2025 Term:  

Prof Yan Yu, Lecture 01:  https://store.cognella.com/98986

Prof Fred Rispoli, Lecture 02: https://store.cognella.com/98984

Prof Silvia Sharna, Lecture 03: https://store.cognella.com/98985

Prof Jinsoo Hwang, Lecture 90:  https://store.cognella.com/99119

 

SUMMER 2025 Term:

TBA

FALL 2025 Term:

 Lecture 01:
Instructor:   Prof. Yan Yu 

Required Course Materials:
"Probability and Statistics for Science and Engineering  with Examples in R" by Hongshik Ahn; 

 

Lecture 02 (Note there are recommended books also listed under Lecture 02 only):
Instructor:  Prof. Matthew Reuter

Required Course Materials:
TBA

Recommended Textbooks:
"Naked Statistics" by Charles Wheelan; W.W. Norton & Company; January 13, 2014, ISBN: 978-0393347777 (paperback)

"Probability and Statistics in Engineering and Science with Examples in R" by Hongshik Ahn; 

 

Lecture 03:
Instructor:  Prof. Hongshik Ahn

Required Course Materials:
"Probability and Statistics for Science and Engineering with Examples in R" by Hongshik Ahn;

 

IF ORDERING THROUGH stonybrook.ecampus.com:

ISBN: 9798823309424 for textbook 

ISBN: 978179394211 for Active Learning Code (free with purchase of textbook)

 

IF ORDERING THROUGH COGNELLA PUBLISHING:

Ebookwith Active Learning accesss:  ISBN: 979-8-8233-0943-1

Paperback with Active Learning accesss:  ISBN: 979-8-8233-0942-4

Ebook only ISBN: 979-8-8233-1405-3

Paperback only ISBN: 979-8-8233-0827-4

Binder-ready/looselef only ISBN: 979-8-8233-0828-1

Active Learning ISBN: 978-1-7935-9421-1

 

If you experience any difficulties, please email orders@cognella.com or call 800.200.3908 ext. 503.

The text includes course material we will reference and use in class regularly, so you should purchase your own copy. Please keep in mind our institution adheres to copyright law. Course materials should never be copied or duplicated in any manner.

 

AMS 310 IS ALSO OFFERED DURING SUMMER SCHOOL. CHECK THE SUMMER SCHOOL BULLETIN FOR TIMES.

Topics

1. Descriptive Statistics (Chapter 1) -- 4 class hours
2. Probability (Chapter 2) -- 5 class hours
3. Discrete Distributions (Chapter 3) -- 7 class hours
4. Continuous Distributions (Chapter 4) -- 6 class hours
5. Multiple Random Variables (Chapter 5) -- 3 class hours
6. Sampling Distributions (Chapter 6) -- 2 class hours
7. Point Estimation and Testing, Introduction (Chapter 7) -- 2 class hours
8. Inferences Based on One Sample (Chapter 8) -- 4 class hours
9. Inferences Based on Two Samples (Chapter 9) -- 2 class hours
10. Examinations and Review -- 7 class hours

 

Learning Outcomes for AMS  310, Survey of Probability and Statistics

1.) Learn and apply descriptive statistical tools in data analysis
        * distinguish between different types of data;
        * use of graphical tools to summarize a given data set;
        * use of numerical methods to summarize a data set.
        * identify the best method to highlight the interesting features in a data set.

2.) Demonstrate and apply an understanding of the basic concepts in probability theory
        * describe the sample space and particular outcomes for some random experiments.
        * use the basic counting techniques to calculate the number of experimental outcomes.
        * calculate probabilities of simple events by working with sets that represents them.
        * apply the axioms of probability to calculate probabilities of compound events.
        * demonstrate an understanding of the differences between various concepts such as disjoint and independence.
        * compute conditional probabilities. 
        * use the law of total probability and Bayes’ rule to calculate probability of complex events.

3.) Demonstrate an understanding of the basic concepts in random variables and their distributions
        * use random variables to model the outcomes of simple experiments.
        * describe the properties of probability mass function and cumulative distribution functions.
        * calculate the means and variances of discrete random variables.
        * learn and apply commonly used discrete distributions such as binomial, geometric, Poisson, and hypergeometric distributions.
        * contrast discrete and continuous random variables.
        * describe the properties of continuous density functions and their cumulative distribution functions. 
        * calculate the means and variances of continuous random variables.
        * learn and apply commonly used density functions such as exponential and normal densities.
        * learn and apply the general properties of the expectation and variance operators.
        * demonstrate an understanding of the connections and differences between different distribution functions, e.g., normal approximation to binomial, Poisson approximation to binomial, and the difference between binomial and hypergeometric distributions.

4.) Use the sampling distribution of a statistic, in particular, the sample mean to:
        * tell the difference between a sample and a population
        * identify the similarities and differences between the normal distribution and the t-distribution.
        * understand and apply the basic concepts in estimation theory such as estimators, bias, variance, and efficiency.
        * construct point estimators (using strong law of large numbers) and interval estimators (in particular, confidence intervals) for estimating the mean of a population.
        * understand and apply confidence intervals.
        * apply the central limit theorem in solving probability questions involving averages from arbitrary distributions.

5.) Use the basic concepts and ideas in inferential statistics, such as hypothesis testing, to”
        * identify the basic components in a classical hypothesis test, including parameters of interest, the null and alternative hypothesis, the rejection region, and test statistics.
        * formulate a given problem as a hypothesis testing problem. 
        * calculate the p-value of a test statistic.
        * conduct the inference for the mean of a population when the underlying variance is either known or unknown.
        * explain the two types of errors and calculate their associated probabilities.