Course_Code1285: Probability and Statistics
Tahir Sher
Fall 2024, M/F 08:00–02:45 PM
Course Description
This course provides an elementary introduction to probability and statistics with applications. Topics include: basic probability models; combinatorics; random variables; discrete and continuous probability distributions; statistical estimation and testing; confidence intervals; and an introduction to linear regression. This course is highly research-oriented and designed for advanced undergraduate in computer science / software engineering / data science / artificial intelligence for research purposes.
Required and Recommended Materials
- T. T. Soong, “Fundamentals of Probability & Statistics for Engineers” WILEY Publishers.
- Pauls. S. Hoel “Introduction To Mathematical Statistics” WILEY Publishers.
- José Unpingco, Python for Probability Statistics and Machine-Learning, Springer Cham.
- Lecture Slides will be provided after each class.
- Research papers will be provided.
Course Components & Grading Policy
The grading policy is subject to minor change.
Student’s grades will be calculated according to the following components:
- Paper/ Project Presentation (20%):
- 20-min presentation on a research paper (30%)
- Class participation (10%)
- Forms for the presentation (1% each, 10 in total)
- Midterm Exam (25%)
- Portion of Statistics included
- Final Exam (45%):
- Portion of Statistics (10%)
- Portion of Probability (25%)
- Sudo code, Project Report (10%).
Paper Presentation Format:
- Select a paper from the provided list
- 20-minute presentation on the selected paper
- 10-minute Q&A session
- Each student must present at least once
- Audience members will submit questions and rate the presenter using a provided form.
Final Project Format:
- 3 students in each group
- Select a topic related to LLMs
- Use IEEE Xplore / Access latex format for proposal and final report
- In-class presentation on the final project
Grading Criteria:
- Paper/ Project Presentation (20%):
- Completeness and quality of the presentation (15%)
- Average peer rating (15%)
- Class Participation (10%):
- Forms submitted for each paper presentation
- Mid / Final Term Exams (70%):
- Assessed the quality of the content / concepts produced and presentation.
Course Schedule
The course schedule is subject to minor change.
| Week | Topics & Reading |
|---|---|
| 1 | Introduction to the subject, concept of population and sample, statistical inference and the role of probability, sampling procedures, data collection |
| 2 | Measures of location and dispersion, graphical presentation of data |
| 3 | Sample space, events, probability of an event, additive rules of probability, Conditional probability, multiplicative rules, Bayes’ rule |
| 4 | Continuation of probability exercises, random variable, discrete probability distributions, continuous probability distributions |
| 5 | Joint probability distributions, mean and variance of random variables, covariance, variance of linear combinations, Chebyshev’s theorem |
| 6 | Uniform, binomial and multinomial distribution, hypergeometric, negative binomial and geometric distributions and their libraries in R / Python / MATLAB |
| 7 | Poisson distribution, continuous uniform distribution, concept of normal distribution, standard normal distribution |
| 8 | Probabilities under normal curve and applications of normal distribution, normal approximation to binomial distribution. Exponential distribution |
| 9 | Midterm Exams |
| 10 | Sampling distribution of mean, central limit theorem. Sampling distribution of the difference between two averages. Sampling distribution of variance |
| 11 | T and F distributions. Concept of estimation, unbiased estimation, interval estimation, confidence interval for mean and proportion |
| 12 | Confidence Interval for the difference of two means and the difference of two proportions. Introduction to hypotheses testing |
| 13 | Testing of hypotheses. Test statistics, two types of error in testing hypotheses, the use of p-value, Testing the mean and proportion in single samples, testing the difference of means and their implementation in their libraries in R / Python / MATLAB |
| 14 | Testing the difference of proportions. test of goodness of fit, test of independence. test of homogeneity, test for several proportions. Announcement of group projects |
| 15 | Simple linear regression, method of least squares. Finding regression coefficients and testing their significance, coefficient of determination , prediction and their libraries in R / Python / MATLAB |
| 16 | (Course Revision) |
| 17 | Final Exams |