EHM454

Course Code: EHM454

Course Name: Communication Theory

Course Objective: This course is an introduction to probability and statistics at the bachelor level for students in computer engineering. This core course is intended to provide a solid general background in probability and statistics.

Course Instructor: Dr. Ferkan YILMAZ { ferkan at yildiz dot edu dot tr }

Course Weekly Plan

• Week 1 Introduction to probability: experiments, sample space, events, counting techniques, additive and multiplicative rules, conditional probability, and Bayes’ rule.

• Week 2 Discrete Random variables and probability distributions: General aspects of discrete and continuous probability distributions, joint distributions, marginal and conditional densities, and statistical independence.

• Week 3 Continuous Random variables and probability distributions: General aspects of discrete and continuous probability distributions, joint distributions, marginal and conditional densities, and statistical independence.

• Week 4 Functions of one or more than one random variables: Distribution function and density function methods, sum of independent Normal random variables,

• Week 5 Mathematical expectation and higher order statistics: Mean, variance, covariance, correlation, moments, Kurtosis, Skewness, and Markov and Chebychev inequalities.

• Week 6 Introduction to Statistics: Population and sample, parameters and statistics,

• Week 7 Simple descriptive statistics: Mean, Median, Quantiles, percentiles, and quartiles, Variance and standard deviation

• Week 8 Midterm (Will be announced)

• Week 9 Frequency Distributions and Histograms, Standard errors of estimates, Standard errors of estimates, Interquartile range, Graphical statistics: Histogram, Stem-and-leaf plot, Boxplot, Scatter plots and time plots

• Week 10 Introduction to Statistical Inference: Population and sample, parameter estimation (Method of moments, and Method of maximum likelihood), Estimation of standard errors,

• Week 11 Confidence intervals: Construction of confidence intervals: a general method, Confidence interval for the population mean, Confidence interval for the difference between two means, Estimating means with a given precision

• Week 12 Unknown standard deviation: Large samples, Confidence intervals for proportions, Estimating proportions with a given precision, Comparison of two populations with unknown variances

• Week 13 Hypothesis testing: Type I and Type II errors (level of significance), Level α tests (general approach), Rejection regions and power, Standard Normal null distribution (Z-test), P-value, Z-tests for means and proportions

• Week 14 Inference about variances: Variance estimator and Chi-square distribution, Confidence interval for the population variance, Comparison of two variances (F-distribution), Confidence interval for the ratio of population variances, F-tests comparing two variances

• Week 15 Final Exam (Will be announced).

Recommended books

• Baron, Michael. Probability and statistics for computer scientists. CRC Press, 2019.

Supplementary books:

• • Ross, Sheldon. Probability and statistics for engineers and scientists. Elsevier, New Delhi, 2009.

  • Scheaffer, Richard L., Madhuri Mulekar, and James T. McClave. Probability and statistics for engineers. Cengage Learning, 2010

  • Soong, Tsu T. Fundamentals of probability and statistics for engineers. John Wiley & Sons, 2004.

Teaching Methods

• Online and Expressive,

• Theoretical-Finding-Centered Discussions

Tentative Assessment and Grading Policy

• Studies in semester Number Contribution (%)

• Midterm Exams 1 40

• Quiz 2 20

• Homework Assignments 0 0

• Final Exam 1 40

• Total 4 100

Attendance

• The absence more than 15 hours will result in failure (F0).

Course Outcomes:

At the end of this course, the student will be able to

• Understand that probability can be employed / utilized to model unpredictability.

• Compute probabilities by using counting / frequency techniques and various probability rules.

• Compute probabilities and joint probabilities by using famous discrete or continuous probability models.

• Understand and apply the Central Limit Theorem.

• Compute mean, variance and correlation for a variety of probability models, and estimate them from data.

• Understand how experiments are designed for collecting data from a group of subjects.

• Ability to represent a data set by Histogram, Stem-and-leaf plot, Boxplot, Scatter plots and time plots.

• Achieve the statistical inference and parameter estimation using samples,

• Understand confidence intervals and how to compute the statistics based on samples.

• Understand hypotheses tests and how to perform them for the mean.

• (November 1, 2020) First homework (Homework 1) announced.