## AMS 310.01 - Survey of Probability and Statistics

### Spring 2020

Instructor: Yan Yu
Office: Math Tower Room 1-104
Lecture: Tuesday, Thursday 7:00am-8:20am; ESS001
Office Hours: Tuesday, Thursday 10:00am-11:00am; Math Tower 1-104
Email: yan.yu@stonybrook.edu
Course Info: 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.
Textbook: Probability and Statistics for Engineering and Science with Examples in R (2nd Edition); Hongshik Ahn
Course Outline:
Ch Topics
1 Describing Data
2 Probability
3 Discrete Distributions
4 Continuous Distributions
5 Multiple Random Variables
6 Sampling Distributions
7 Introduction to Point Estimation and Testing
8 Inferences Based on One Sample
9 Inferences Based on Two Sample
Learning Outcomes:
• 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.
• 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 BayesÂ’ rule to calculate probability of complex events.
• 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.
• 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.
• 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.
Exams: Midterm-1 Tuesday, 03/03/2020
Midterm-2 Tuesday, 04/14/2020
Final Wednesday, 05/20/2020, 8:30pm - 11:00pm
TAs: Siao Lu
E-mail: siao.lu@stonybrook.edu
Office Hours: Tu/Th 11am-12pm
Office Hours Room: Harriman Hall 132

Ziyong Zhang
E-mail: ziyong.zhang@stonybrook.edu
Office Hours: M/W 2-3pm
Office Hours Room: Harriman Hall 132

Michael Sweeney
E-mail: michael.d.sweeney@stonybrook.edu
Office Hours: M/W 6-7pm
Office Hours Room: Harriman Hall 132

Qingyue Chen
E-mail: qingyue.chen@stonybrook.edu
Office Hours: M/W 10-11am
Office Hours Room: Harriman Hall 132

Ersha Kumar
E-mail: ersha.kumar@stonybrook.edu
Office Hours: Tu 2-4pm
Office Hours Room: Harriman Hall 132

Harshit Kapur
E-mail: harshit.kapur@stonybrook.edu
Office Hours: M 3:30-5:30pm
Office Hours Room: Harriman Hall 132

Siyuan Zou
E-mail: siyuan.zou.1@stonybrook.edu
Office Hours: Th 3-5pm
Office Hours Room: Harriman Hall 132

Policies
• Homework assignments given regularly on Cognella Active Learning ans Blackboard, due at the beginning of class on the due date. For full credit, please write down all intermediate steps needed, not just final answers.
• Late homework is an automatic zero.
• All exams will be in class, closed notes and book. A letter-sized hand-written (not typed or xeroxed) formula sheet and a non-graphing calculator will be allowed in the exam.
• Exams will start at the beginning of class; come early so you are prepared.
• All exams will be held in regular classroom, unless stated otherwise.
• 20% Homework - The lowest homework score will be dropped
• 25% Midterm-1
• 25% Midterm-2
• 30% Final
Lower Division Upper Division
A's 25% 30%
B's 30% 35%
C's 25% 25%
D's 10% 5%
F's 10% 5%
Disability Act: If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential. [In addition, this statement on emergency evacuation is often included, but not required: Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website:http://www.stonybrook.edu/ehs/fire/disabilities ]
Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.
Homework Homework # 4 - Due: 3/12/2020
3.3, 3.6, 3.9, 3.20, 3.25
3.32, 3.35, 3.44

Homework # 5 - Due: 3/31/2020
3.48, 3.54, 3.57, 3.61
4.4, 4.12, 4.16, 4.21, 4.26

Homework # 6 - Due: 4/7/2020
4.28, 4.36, 4.37, 4.51, 4.53
5.2, 5.5, 5.12, 5.14

Homework # 7 - Due: 4/23/2020
5.18, 5.21, 5.29, 5.30
6.4, 6.9, 6.14