## COURSE OBJECTIVES

1. The course will provide knowledge and skills for the students to apply statistical techniques to complex engineering problems
2. This course will provide knowledge regarding Probability Theory, Random Variables, Distributions and Estimation, emphasizing the link between Statistics and Engineering.
3. Students are expected to develop a statistical way of thinking and ability for the successful usage of the statistical concept, theory and notations.

## COURSE LEARNING OUTCOMES (CLO)

CLO-1: Explain the use of descriptive techniques to describe the statistical data. (C2)
CLO-2: Use the concepts and methods of probability theory for solving problems in engineering sciences. (C3)
CLO-3: Infers the population parameters on the basis of sample study using the techniques of inferential statistics. (C4)

## COURSE CONTENTS

1. Introduction and Descriptive Statistics – Six Lectures

• What is statistics, Types of statistics
• Methods for Describing Sets of Data
• Graphical Methods for Describing Quantitative Data. Pareto Diagrams and Dot Diagrams
• Frequency Distributions. Histograms,
• Quantitative Data, Multivariate Data.
• Measures of Location, the Mean, Median and Mode. Quartiles Percentiles.
• Measures of Variability. Range, Mean (Absolute) Deviation, Standard Deviations
• Skewness and coefficient of Skewness
• Chebyshev’s Theorem, Empirical Rule
• Coefficient of Variation
• Measures of Relative Standing, The pth Percentile, z-scores.

2. Probability – Six Lectures

• Random Experiment, Event, Sample Spaces and Probability
• Axioms, Interpretations and Properties of Probability
• The Additive Rule and Mutually Exclusive Events
• Complementary Events
• Counting Techniques
• Conditional Probability
• The Multiplicative Rule and Independent Event
• Law of Total Probability
• Prior and Posterior Probabilities, Bayes’ Rule.

3. Random Variables and Probability Distributions – Five Lectures

• Random Variables, Discrete and Continuous
• Discrete Probability Distributions
• Mathematical Expectations, or Expected Value of Discrete r. v’s
• Binomial Experiment
• The Binomial Probability Distribution
• The Poisson Probability Distribution

4. Continuous Random Variable – Five Lectures

• Continuous Probability Distributions
• The Uniform Distribution
• The Normal Distributive
• Approximating A Binomial Distribution with A Normal Distribution
• Other Continuous Distributions

5. Sampling Distributions – Five Lectures

• Introduction to Sampling Distributions. Properties
• The Sampling Distribution of the Sample Mean (σ known)
• The Sampling Distribution of the Sample Mean (σ unknown)
• The Sampling Distribution of the Variance
• t-Distribution and Chi-Square Distribution

6. Regression Analysis – Five Lectures

• Probabilistic Modals and Curve Fitting
• Fitting the Model (Method of Least Squares)
• Estimating Model Parameters. Correlation (Measure of Usefulness Of Model)
• The Coefficient of Determination
• Multiple Regression