This course introduces fundamental concepts of probability and statistics, emphasizing applications in engineering problem-solving. Students will develop an understanding of probability theory, random variables, probability distributions, and statistical inference techniques. The course covers topics such as basic probability theory, estimation, hypothesis testing, and regression analysis.

Through theoretical exploration and practical examples, students will learn to apply probabilistic models to analyze uncertainty in engineering systems and make data-driven decisions. Emphasis is placed on developing statistical reasoning, using appropriate methods to model real-world data, and interpreting results effectively.

By the end of the course, students will be able to compute probabilities, analyze data using descriptive and inferential statistics, and apply statistical tools to engineering applications. The course prepares students for real-world problem-solving and equips them with the skills necessary to critically assess variability in engineering processes. Additionally, students will gain experience in Python libraries for data analysis, reinforcing both theoretical knowledge and practical implementation.

There is no prerequisite course for this class.

Attendance 10%
Homework 20%
Midterm 30%
Final 40%
TOTAL 100%

전치혁, 정민근, 이혜선, 공학응용통계, 홍릉과학출판사, 3rd edition, 2023.

Probability

Week 1 Chapter 1: Introduction to Statistics and Data Analysis
Chapter 2: Probability
- Rules of Calculating Probabilities
- Bayes' Rule

Week 2 Chapter 3: Random Variables and Probability Distributions
- Discrete vs. Continuous
- Joint / Conditional / Marginal

Week 3 Chapter 4: Mathematical Expectation
- Mean /Variance / Covariance
- Chebyshev's Theorem

Week 4/5 Chapter 5: Some Discrete Probability Distributions
- Uniform / Bernoulli / Binomial / Multinomial
- Hypergeometric / Geometric / Negative Binomial / Poisson

Week 5/6 Chapter 6: Some Continuous Probability Distributions
- Uniform / Normal
- Exponential / Gamma / Chi-Squared, Weibull, Beta, etc.

Week 7/8 Chapter 7: Functions of Random Variables
- Transformations

Statistics

Week 8/9 Chapter 8: Random Sampling
- Sample Statistics/ Sampling Distributions: t distribution,
- F distribution

Week 10/11 Chapter 9: One- and Two-Sample Estimation Problems
- Methods of estimation
- Estimating Mean / Difference between two means / Proportion /
Variance / Ratio of Two Variances

Week 12/13 Chapter 10: One- and Two-Sample Tests of Hypotheses
- Tests concerning means / Proportions / Difference between Two
proportions / Variances
- Goodness-of-fit Test / Test for independence

Week 14/15 Chapter 11: Simple Linear Regression and Correlation
- Correlation / Least Squares
- Inferences concerning regression coefficients/ ANOVA

Lecture based class

STC Course