Syllabus

• Instructor: Art Diky

• Office Hours: Tue 5:00PM - 6:00PM, NAC 7/101

• Email: adiky at gradcenter.cuny.edu

• Textbook: Michael Baron, ”Probability and Statistics for Computer Scientists”, CRC Press, 2007 (ISBN: 1-58488-641-2)

• Supplementary material: Sheldon M. Ross, ”Introduction to Probability and Statistics for Engineers and Scientists,” 4rth Edition, Elsevier Academic Press, 2009 (ISBN: 978-0-12-370483-2)

• Lecture Notes: https://wildart.github.io/CSC21700

Objective

The objective of this course is to help you learn to analyze data and use methods of statistical inference. Central to the course is the application of fundamental concepts covered in probability and decision making to the problem of drawing inferences from data on observed outcomes. Topics covered during the first part of the course will include statistical sampling and sampling distributions, point estimation and confidence intervals, hypothesis testing, correlations among variables, and regression. The second part of the course will focus on multivariate analysis, with special attention paid to the inferences that may drawn with respect to prediction and causality.

Prerequisites

• Computer Science 104, Calculus I.

Grading

• Assignments: 20%

• Project: 30%

• Midterm exam: 20%

• Final exam: 30%

Course Outline

1. Probability

   • Sample space, events, and probability

   • Rules of Probability

   • Equally likely outcomes. Combinatorics.

   • Conditional Probability. Independence

2. Discrete Random Variables and their Distributions

   • Distribution of a random variable

   • Distribution of a random vector

   • Expectation and variance

   • Families of discrete distributions

3. Continuous Distributions

   • Probability density

   • Families of continuous distributions

   • Central Limit Theorem

   • Midterm

4. Computer Simulations and Monte Carlo Methods

   • Simulation of random variables

   • Solving problems by Monte Carlo methods

5. Introduction to Statistics

   • Population and sample, parameters and statistics

   • Simple descriptive statistics

   • Graphical statistics

6. Statistical Inference

   • Parameter estimation

   • Confidence intervals

   • Unknown standard deviation

   • Hypothesis testing

   • Bayesian estimation and hypothesis testing

7. Regression

   • Least squares estimation

   • Analysis of variance, prediction, and further inference

   • Multivariate regression

   • Model building

Course Outcomes

1. Knowledge of descriptive statistics and the ability to describe real, everyday data by using the concept of sample mean and variance, correlation coefficient.

2. Knowledge of probability concepts and the ability to apply probability theory to gain insight into real problems and situations and to applications like simulation.

3. Knowledge of random variables, expectation and their use in applications.

4. Knowledge of the basic concepts in computer simulation, central limit theorem and the distribution of sample statistics.

5. Team programming project illustrating basic statistical techniques, with written and oral presentations.