The objective of this Probability and Statistics course is to equip students with foundational knowledge in probability theory and statistical methods, focusing on core concepts essential for engineering applications. Students will develop essential skills in statistical data analysis, enabling them to apply various statistical techniques to address real-world engineering challenges.

Additionally, the course emphasizes the interpretation and effective communication of statistical results, preparing students to make informed, data-driven decisions in their professional practice. Key learning outcomes include understanding probability distributions, statistical inference methods, correlation and regression analysis, and quality control techniques.

1.1 Introduction to statistics and its importance in engineering

1.2 Measure of central tendency and measure of variation

1.3 Graphical representation of data: Histograms, box plots and scatter plots

1.4 Basic probability concepts, additive law, multiplicative law

1.5 Conditional probability and Bayes’ theorem

2.1 Random variables: Discrete and continuous

2.2 Expectation and variance of discrete and continuous random variables

2.3 Discrete probability distributions: Binomial, Poisson, negative Binomial

2.4 Continuous probability distributions: Normal, Gamma, Chi-Square

2.5 Population and sample

2.6 Sampling distribution of mean and proportion

2.7 Central limit theorem

3.1 Point estimations and properties of estimators

3.2 Confidence intervals for mean and proportions

3.3 Hypothesis testing, parametric and non-parametric tests, procedure of hypothesis

3.4 Hypothesis testing of mean (Single mean, two means, paired t-test and one-way)

3.5 Goodness of fit tests and independence of attributes (Chi-square and Kolmogorov-Smirnov test)

4.1 Correlation analysis and test of linear correlation

4.2 Simple regression analysis, the concept of explained, unexplained, and total variation

4.3 Multiple regression analysis

5.1 Quality control and its importance in engineering

5.2 Control charts for variables (X-bar, R-chart, P-chart)

5.3 Six sigma concepts

The Probability and Statistics tutorials include practical exercises to reinforce theoretical concepts. Students will work with real-world engineering datasets to develop hands-on experience with statistical analysis techniques.

Visualize engineering data using appropriate graphical representations. Compute measures of central tendency and variation for given datasets. Solve probability problems including conditional probability and Bayes’ theorem applications.

Solve engineering problems involving discrete and continuous probability distributions. Calculate expectations and variances for different random variables. Apply the central limit theorem to sampling problems.

Construct confidence intervals for engineering applications. Perform hypothesis tests on means (single mean, two means, paired t-test). Conduct goodness-of-fit tests and tests of independence using Chi-square and Kolmogorov-Smirnov tests.

Calculate correlation coefficients and perform significance tests. Fit and interpret simple and multiple regression models to engineering data. Analyze variance components in regression models.

Construct and interpret control charts for process monitoring. Apply six sigma concepts to quality improvement scenarios. Analyze process capability using statistical methods.

Based on new syllabus of IoE (2080), II year II part

Essential Probability and Statistics textbooks for engineering students