Probability and Statistics

Syllabus

1. Descriptive Statistics and Basic Probability (6 hours)
   1. Introduction to statistics and its importance in engineering
   2. Measure of central tendency and measure of variation
   3. Graphical representation of data: histograms, box plots and scatter plots
   4. Basic probability concepts, additive law, multiplicative law
   5. Conditional probability and Bayes' theorem
2. Probability Distributions and Sampling Distribution (14 hours)
   1. Random variables: discrete and continuous
   2. Expectation and variance of discrete and continuous random variables
   3. Discrete probability distributions: Binomial, Poisson, negative Binomial
   4. Continuous probability distributions: Normal, Gamma, Chi-Square
   5. Population and sample
   6. Sampling distribution of mean and proportion
   7. Central limit theorem
3. Statistical Inference (14 hours)
   1. Point estimations and properties of estimators
   2. Confidence intervals for mean and proportions
   3. Hypothesis testing, parametric and non-parametric tests, procedure of hypothesis
   4. Hypothesis testing of mean (single mean, two means, paired t-test and one-way)
   5. Goodness of fit tests and independence of attributes (Chi-square and Kolmogorov-Smirnov test)
4. Correlation and Regression (6 hours)
   1. Correlation analysis and test of linear correlation
   2. Simple regression analysis, the concept of explained, unexplained, and total variation
   3. Multiple regression analysis
5. Statistical Quality Control (5 hours)
   1. Quality control and its importance in engineering
   2. Control charts for variables (X-bar, R-chart, P-chart)
   3. Six sigma concepts

Practicals

1. Visualize data, compute central tendency and variance in engineering problems using computer software
2. Solve engineering problems involving probability
3. Solve engineering problems involving discrete probability distribution and its interpretation
4. Solve engineering problems involving continuous probability distribution and its interpretation
5. Analyze numerical engineering datasets, perform normality tests, confidence intervals, significance tests of means, and ANOVA
6. Analyze categorical engineering datasets, perform crosstabulation, proportion tests, Chi-Square tests
7. Calculate the correlation coefficient and perform correlation tests on engineering data
8. Fit and interpret simple and multiple regression models on engineering data using computer software
9. Use control charts for process monitoring on sample engineering data
10. Create control charts using computer software