Applied Probability and Statistics

• Basic Probability Concepts: Sample Space and Events Definitions  of Probability, Elementary Set Theory

• Properties of Probability, Conditional Probability, Independent Events

• Basic Combinatorial Analysis, Reliability Applications

• Random variables: Definition of Random Variable, Events Defined by Random Variables, Distribution Functions, Discrete Random Variables.

• Special Probability Distributions: The Bernoulli Trial and Bernoulli Distribution, Binomial Distribution, Geometric Distribution, Poisson Distribution

• Continuous Random Variables, Exponential Distribution, Uniform Distribution.

• Normal Distribution.

• Multiple Random Variables: Joint CDFs of Bivariate Random Variables, Discrete Bivariate Random Variables and Continuous Bivariate Random Variables

• Determining Probabilities from a Joint CDF, Conditional Distributions

• Functions of Random Variables: Functions of One Random Variable, Moment Generating Function. The s-Transform

• The z-Transform, Statistics Numerical Descriptive Measures and Simple Linear Regression

• Numerical Descriptive Measures and Simple Linear Regression

• Confidence Intervals of the Mean

• Confidence Intervals of the Mean, Hypothesis Testing

• Hypothesis Testing

ABET’s course outcomes (1-7) criteria

1. Engineering programs must demonstrate that their graduates have:

an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.

    2. an ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors.

     3. an ability to communicate effectively with a range of audiences.

  4. an ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.

   5. an ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.

   6. an ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.

   7. an ability to acquire and apply new knowledge as needed, using appropriate learning strategies.

• Elementary set theory

• Properties of probability

• Independent events

• Combinatorial analysis

• Reliability applications

• Random Variables

• Continuous random variables

• Expected value of random variables

• Geometric and Poisson distributions

• Normal distribution

• Problem Solving:  Random Variables                                            Radnom Variables_Chapter_2

• Review of: Double integrals and polar coordinates

• Multiple Random Variables 1

• Continuous Bivariate R.V. Problem Solving Part I

• Continuous Bivariate R.V. Problem Solving Part II

• Functions of R.V. Problem Solving

• The Z-transform

• Basic Statistics

• Hypothesis testing

• Course outline

• First week videos: Elementary set theory and Properties of probability

• Second week videos: Independent events and Combinatorial analysis.

• Third week videos:  Reliability application and Random variables.

• Fourth week videos: Continuous random variables and Expected value of random variables

• Fifth week video: Geometric and Poisson distributions

• Sixth week video: Normal distribution

• Seventh week video:  Review of: Double integrals and polar coordinates

• 8th week: Multiple Random Variables 1

• Course outline

• 9-10-2024: Elementary set theory and Properties of probability

• 17-10-2024: Independent events and Combinatorial analysis.

• 24-10-2024:  Reliability application and Random variables.

• 31-10-2024: Continuous random variables and Expected value of random variables

• 7-11-2024: Problem solving Radnom Variables_Chapter_2

• 14-11-2024:  Geometric and Poisson distributions

• 21-11-2024: Normal distribution

• 28-11-2024: Multiple Random Variables 1

• 5-12-2024: Continuous Bivariate R.V. Problem Solving Part I                                                     Continuous Bivariate R.V. Problem Solving Part II

• 12-12-2024: Functions of R.V. Problem Solving                 The Z-transform

• 19-12-2024: Basic Statistics

• 9-1-2025: Hypothesis testing