Syllabus
Course Description
This course on uncertainty in engineering analysis can also be referred to as probability and statistics for engineers. In particular, we will deal with the applications of probability and statistics to problems related to civil and environmental engineering.
ABET Program Outcomes for the Class
These outcomes are based on the accreditation requirements from the Accreditation Board for Engineering and Technology, Inc. (
ABET
). The expected criteria for this class are the following:
Upon successful completion of the undergraduate program for Civil Engineering at Utah State University, students will have:
- Proven themselves proficient in mathematics, the sciences, and the structures, geotechnical, hydraulics, environmental and transportation areas of civil engineering.
- Demonstrated the ability to solve engineering problems, utilizing fundamental engineering principles as well as the latest technologies and engineering tools, in the process of engineering analysis and design. They will have done this as individuals and as members of multi-disciplinary teams.
- Outcome 3. Shown a capacity for investigation and experimentation into physical (engineering) phenomena along with the ability to analyze and interpret engineering data in at least two of the following areas of civil engineering: structures, geotechnical, hydraulics, environmental, and transportation.
Prerequisites
To understand and apply concepts of probability and statistics you need to have taken basic math classes such as Algebra and Calculus (uni-variate differential and integral Calculus is essential, multi-variate Calculus is useful).
Required Textbook
No textbook required. We will use a set of class notes produced by Dr. Urroz.
Class Contents
- Introduction (UNIT 1)
- Class description
- Probability and statistics in Civil and Environmental Engineering
PROBABILITY
- Probability (UNIT 2)
- Sample spaces and events
- Definitions of probability
- Axioms and theorems
- Conditional probability
- Bayes Theorem
- Basic combinatorial analysis
- Random variables (UNIT 3)
- Discrete and continuous single random variables
- Probability mass function (pmf), Cumulative distribution function (CDF)
- Probability density function (pdf), Cumulative density function (CDF)
- Mathematical expectation
- Variance
- Other parameters
- Discrete and continuous multiple random variables
- Parametric probability distributions (UNIT 4)
- The normal distribution
- Discrete distributions
- Continuous distributions
- Distributions used in statistical inference
- Random numbers and statistical simulation
STATISTICS OF SAMPLES, STATISTICAL GRAPHS
- Numerical samples and data reduction (UNIT 5)
- Statistics of a sample
- Measures of central tendency
- Measures of spread
- Measures that split the data
- Dotplots and boxplots
- Frequency distributions
- Frequency tables
- Histograms and ogives
- Statistical graphs
- Statistics of grouped data
- Propagation of errors in measurements
REGRESION and DATA FITTING
- Regression techniques (UNIT 6)
- Linear regression
- Non-linear regression
- Multiple linear regression
STATISTICAL INFERENCE
- Sampling theory (UNIT 7)
- Sampling theory
- Sampling distribution of means
- Sampling distributions of proportions
- Sampling distribution of variances
- Sampling distribution of ratios of variances
- Estimation theory and hypothesis testing (UNIT 8)
- Statistical hypotheses, null hypotheses
- Tests of hypotheses and significance
- Type I and Type II errors
- Level of significance
- One-tailed and two-tailed tests
- P-value
- Large and small samples
- Operating characteristic curves
- Power of a testing
- Confidence intervals