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:
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FALL 2023 Term:
Prof. Yan Yu, Lecture 01: Revised 2nd Edition textbook + Active Learning courseware update: https://store.cognella.com/96781
Prof. Matthew Reuter, Lecture 02: Revised 2nd Edition textbook + Active Learning courseware update: https://store.cognella.com/96782
Prof. Fred Rispoli, Lecture 03: Revised 2nd Edition textbook + Active Learning courseware update: https://store.cognella.com/96780
Prof. Myoungshic Jhun, SUNY Korea: Revised 2nd Edition textbook + Active Learning courseware update: https://store.cognella.com/96785
WINTER 2024 Term:
Prof. Fred Rispoli, Lecture 30: Revised 2nd Edition textbook + Active Learning courseware update: https://store.cognella.com/97553
SPRING 2024 Term:
Prof. Yan Yu, Lecture 01: Revised 2nd Edition textbook + Active Learning courseware update: https://store.cognella.com/97556
Prof. Fred Rispoli Lectures 02 and 03: Revised 2nd Edition textbook + Active Learning courseware update: https://store.cognella.com/97557
Prof. Hongshik Ahn, SUNY Korea: Revised 2nd Edition textbook + Active Learning courseware update: https://store.cognella.com/97552
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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.