Probability and Statistics for Engineers: 15-Week Course Outline

Module 1: Introduction to Probability and Statistics in Engineering

• Role of statistics in engineering decision-making

• Types of data and measurement scales

• Basic concepts: population vs. sample, parameters vs. statistics

• Engineering applications and case studies

• Introduction to statistical software tools

Module 2: Descriptive Statistics

• Measures of central tendency (mean, median, mode)

• Measures of dispersion (range, variance, standard deviation)

• Data visualization techniques for engineers

• Stem-and-leaf plots, box plots, histograms

• Interpreting statistical summaries in engineering contexts

Module 3: Probability Concepts

• Basic probability axioms and rules

• Sample spaces and events

• Mutually exclusive and independent events

• Conditional probability

• Engineering reliability problems

Module 4: Probability Distributions - Discrete

• Random variables and probability mass functions

• Expected value and variance

• Bernoulli and binomial distributions

• Poisson distribution and applications

• Hypergeometric distribution

Module 5: Probability Distributions - Continuous

• Probability density functions

• Cumulative distribution functions

• Normal distribution and applications

• Exponential and Weibull distributions

• Lognormal distribution in engineering applications

Module 6: Sampling Distributions

• Central Limit Theorem and its implications

• Distribution of sample means

• Standard error

• Confidence intervals

• Sample size determination

Module 7: Point Estimation and Confidence Intervals

• Properties of good estimators (unbiasedness, efficiency, consistency)

• Maximum likelihood estimation

• Confidence intervals for means

• Confidence intervals for proportions

• Tolerance intervals in engineering applications

Module 8: Introduction to Hypothesis Testing

• Null and alternative hypotheses

• Type I and Type II errors

• p-values and significance levels

• Power analysis

• Statistical vs. practical significance

Module 9: Hypothesis Tests for a Single Sample

• z-tests and t-tests for means

• Tests for proportions

• Chi-square tests for variance

• Engineering case studies with single sample tests

• Sample size and power calculations

Module 10: Hypothesis Tests for Two Samples

• Independent samples t-test

• Paired samples t-test

• F-test for comparing variances

• Tests for comparing proportions

• Non-parametric alternatives

Module 11: Introduction to Regression Analysis

• Simple linear regression model

• Least squares estimation

• Regression assumptions

• Coefficient of determination (R²)

• Interpreting regression outputs

Module 12: Multiple Regression Analysis

• Multiple regression models

• Parameter estimation and interpretation

• Model selection techniques

• Multicollinearity

• Polynomial regression

Module 13: Regression Model Validation

• Residual analysis

• Influence diagnostics

• Transformations

• Cross-validation techniques

• Prediction intervals

Module 14: Analysis of Variance (ANOVA)

• One-way ANOVA

• Multiple comparisons

• Two-way ANOVA

• Interaction effects

• ANOVA applications in engineering experiments

Module 15: Advanced Topics and Engineering Applications

• Design of experiments basics

• Statistical quality control introduction

• Bootstrap methods

• Bayesian statistics introduction

• Final project presentations and course review

Each module should include:

• Theory and concepts

• Computational examples

• Engineering-specific applications

• Hands-on activities or lab exercises

• Assessment components