1. Prerequisites

:

None

2. Objectives

:

This course provides an introduction to some concepts of probability and statistics with applications for students who would like to have careers in information intensive fields.

3. Textbook/
Lecture notes

:

- Probability & Statistics for Engineers & Scientists, R.E.Walpole, R.H. Myers, S.L. Myers, K.Ye, Prentice Hall, 2007 or 2012.

- First Course in Probability, M.R. Sheldon, Prentice Hall, 2010.

- Applied Statistics and Probability for Engineers,  D.C. Montgomery, G.C.Runger,  John Wiley & Sons, 2007.

4. Attendance

:

Compulsory attendance for lectures is 70%

5. Grading

:

Assignments & Quizzes 30%,
Midterm 30%,
Final 40%

6. Academic
dishonesty

:

Academic dishonesty is related to cheating and plagiarism. Copying in whole or in part others’ assignments, or exams, is considered cheating respectively plagiarism. All parties involved will receive a zero score for  assignments or the exam.

Week

Topics

Assignments

1

Syllabus & Introduction

2

Introduction to Statistics and Data Analysis

3

Probability

Probability of an Event,  Counting Rules, Conditional Probability, Bayes’ Rule

Quiz 1

4

Random Variables & Probability Distributions

Concept of a Random Variable,  Discrete Probability Distributions, Continuous Probability Distributions, Joint Probability Distributions

5

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

Quiz 2

6

Some Discrete Probability Distributions

Discrete Uniform, Binomial, Multinomial, Hypergeometric, Negative Binomial, Geometric, and Poisson Distributions,

The Poisson Process

7

Some Continuous Probability Distributions

Continuous Uniform, Normal, Gamma, Exponential, Chi-Squared, and Lognormal Distributions,

Normal Approximation to the Binomial

8

Fundamental Sampling Distributions and Data Descriptions

Random Sampling

Data Displays and Graphical Methods

Sampling Distributions of Means, and S²

Central Limit Theorem

t-Distribution and F-Distribution

Quiz 3

9

MIDTERM

10

One-Sample Estimation Problems

Statistical Inference

Classical Methods of Estimation

Estimating the Mean and the Variance

Prediction Intervals and Tolerance Limits

Estimating a Proportion

11

Two-Sample Estimation Problems

Estimating the Difference between Two Means and Two Proportions

Estimating the Ratio of Two Variances

Maximum Likelihood Estimation

Quiz 4

12 

13

One-Sample Tests of Hypothesis

Statistical Hypotheses: General Concepts

Testing a Statistical Hypothesis

One- and Two-Tailed Tests

The Use of P-value for Decision Making

Tests Concerning a Single Mean and a Single Proportion

Two- Sample Tests of Hypothesis

Tests on Two-Means and  Two Proportions

Choice of Sample Size for Testing Means

14

Graphical Methods for Comparing Means

One- and Two-Sample Tests Concerning Variances

Goodness-of-Fit Test and Test for Homogeneity

Testing for Several Proportions

Quiz 5