At the end of this course, the students; 1) Describe basic premises of Probability Theory 2) Analyze datasets by calculating statistics to infer about probabilistic concepts 3) Interpret by applying numerical and graphical methods used in summarizing statistics data sets 4) Learn and apply the concepts of probability and distribution functions of random variables 5) Have the ability to select and apply some discrete and continuous probability distributions in accordance with the problems and associate them with real life problems 6) Have the ability to determine the distribution of functions of random variables and relate them to the concept of sampling distribution 7) Have the ability to define basic concepts of statistics (mass, sampling, random sampling, sampling distribution, etc.)
MODE OF DELIVERY
Face to face
PRE-REQUISITES OF THE COURSE
No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT
COURSE DEFINITION
Displays of Data Sets and Calculations of Some Important Statistics; Fundamentals of Probability; Definition of Probability, Conditional Probability, Bayes' Theorem and Independent Events; Concept of Random Variable, Probability Distributions; Discrete and Continuous Probability Distributions; Joint Probability Distributions, Statistical Independence; Mathematical Expectation, Variance and Covariance; Some Discrete Probability Distributions; Some Continuous Probability Distributions; Functions of Random Variables, Distribution Function Technique; Change of Variables Technique (For one and two random variables); Moment Generating Function Technique, Definition of Random Sampling Concept of Random Sampling, Sampling Distributions for Some Statistics; Regression analysis.
COURSE CONTENTS
WEEK
TOPICS
1st Week
Representation of Data Sets and Calculation of Some Important Statistics
2nd Week
Basic Concepts of Probability
3rd Week
Definition of Probability, Conditional Probability, Bayes Theorem and Independent Events
4th Week
Concept of Random Variable, Probability Functions of Random Variables
5th Week
Discrete Distributions, Continuous Distributions
6th Week
Compound Probability Distributions, Statistical Independence
7th Week
Mathematical Expected Value, Variance and Covariance
8th Week
Midterm exam
9th Week
Special Discrete Distributions
10th Week
Special Continuous Distributions
11th Week
Determination of Distribution of Functions of Random Variables, Distribution Function Technique
12th Week
Variable Conversion Technique (For Single and Two Variables)
13th Week
Moment Generating Function Technique, Random Sampling Concept Statistics
14th Week
Random Sampling, Sampling Distributions, Some Basic Sampling Distributions
RECOMENDED OR REQUIRED READING
Reference: Ang, A.H-S., and W.H. Tang, Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering, 2nd edition, John Wiley & Sons, 2007. Walpole, R.E., Myers, R.H., Myers Sh. L., Ye K., Probability and Statistics or Engineers and Scientists Prentice Hall, 7th edition. Additional Resources: Pishro-Nik, H., Introduction to Probability, Statistics, and Random Processes, Kappa Research, LLC, 2014.
