Probability & Statistics

• Course Title: Probability and Statistics (MTS603)
• Credit Hours: 03
• Prerequisite: None

Introduction

This course begins by introducing  basic concepts of data and its types. Topics on various methods and procedures of collecting, organizing, summarizing, presenting and analyzing the data are presented. Topics on relationship between two variables such as Regression and Correlation analysis are covered. The second portion of the course focuses on the probability theory. From the basic probability rules to the construction of all the well-known probability distributions like binomial, hyper-geometric, uniform and normal distributions are discussed. The course will finally introduce the inferential statistics which is further divided into estimation and hypothesis testing. It deals with the drawing of conclusions about various phenomena on the basis of real data collected on sample basis. The use of appropriate methods like Z-test, T-test, F-test, Chi-square test are explained with examples.

Learning Objectives

At the end of the course, you students should be able to understand:

    • Basic concepts of data and its types

    • Methods for collecting, presenting and summarizing data

    • Methodologies for regression and correlation analysis for future predictions

    • Basic concepts and rules of probability along with important probability distributions

    • Sampling concept, its types and techniques

    • Estimating and hypothesis testing using main distributions

    • Fundamental  skills for basic statistical computing using R.

Course Content:

• Introduction to Statistics and Data Analysis
•  Statistical Inference, Samples, Populations,and the Role of Probability.
•  Sampling Procedures. Discrete and Continuous Data. 
• Statistical Modeling. Types of Statistical Studies. 
• Probability: Sample Space, Events,Counting Sample Points, Probability of an Event, Additive Rules, Conditional Probability, Independence, and the Product Rule, Bayes’ Rule.
•  Random Variables and Probability Distributions. Mathematical Expectation: Mean of a Random Variable, Variance and Covariance of Random Variables, Means and Variances of Linear Combinations of Random Variables, Chebyshev’s Theorem. 
• Discrete Probability Distributions. Continuous Probability Distributions. 
• Fundamental Sampling Distributions and Data Descriptions: Random Sampling, Sampling Distributions, Sampling Distribution of Means and the Central Limit Theorem. Sampling Distribution of S2, t-Distribution, F-Quantile and Probability Plots. 
• Single Sample & One- and Two-Sample Estimation Problems. Single Sample & One- and Two-Sample Tests of Hypotheses. 
• The Use of P-Values for Decision Making in Testing Hypotheses (Single Sample & One- and Two-Sample Tests)
• Linear Regression and Correlation. Least Squares and the Fitted Model,
• Multiple Linear Regression and Certain, Nonlinear Regression Models, Linear Regression Model Using Matrices, Properties of the Least Squares Estimators.

Grading Policy:

• Quizzes (LMS): 10%
• Assignments/ Reports(LMS): 15%
• Attendance + LMS Log: 10%
• Discussion Forum / Video / Audio Engagement: 15%
• Mid Term Exam(Oral Exams and Presentations): 20%
• Final Exam(Oral Exams and Presentations): 30%

Reference Materials:

1. Probability and Statistics for Engineers and Scientists by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying E. Ye, Pearson; 9th Edition (January 6, 2011). ISBN-10: 0321629116
2. Probability and Statistics for Engineers and Scientists by Anthony J. Hayter, Duxbury Press; 3rd Edition (February 3, 2006), ISBN-10:0495107573
3. Schaum's Outline of Probability and Statistics, by John Schiller, R. Alu Srinivasan and Murray Spiegel, McGraw-Hill; 3rd Edition (2008). ISBN-10:0071544259