Course Description
Introduction to the field of probability and statistics with an
emphasis on topics and problems relevant to engineering.
Students will learn how to calculate probabilities and
probability distributions for stochastic processes. Measurement
systems and communication systems will be among the
probabilistic systems considered.
Athena Title
Probability and Stat for Engr
Prerequisite
MATH 2260
Semester Course Offered
Offered every year.
Grading System
A - F (Traditional)
Student Learning Outcomes
- By the end of this course, a successful student will understand the uncertainty inherent to collection of data.
- By the end of this course, a successful student will understand simulation and analysis within uncertainty.
- By the end of this course, a successful student will understand the principles and concepts of probability and statistics in analyzing and designing engineering systems.
- By the end of this course, a successful student will understand a systematic technique for describing uncertainty.
- By the end of this course, a successful student will understand quantitative methods for describing direct and indirect relationships among variables.
Topical Outline
- 1) Descriptive statistics
a) Means, medians, variance, co-variance, percentiles
- 2) Programming in R
a) R language
b) Vectors and matrices in R
c) Variables, arrays, and scripts
d) Loops
- 3) Probability
a) Sample spaces
b) Assigning probabilities
c) Outcomes
d) Distributions
e) Random variables in environmental applications
f) Independent events
g) Joint and conditional probabilities
h) Repeated trials
- 4) Combinatorics
a) Combinatorial methods
b) Combinatorial techniques for evaluating probability
- 5) Simulation (covered primarily in the laboratory)
a) Stochastic
b) Monte Carlo
c) Deterministic
d) Probability distributions
e) Expectation
f) Population mean and variance
- 6) Data fitting (primarily in laboratory)
- 7) Error associated with measurements
- 8) Error propagation
- 9) Central Limit Theorem
- 10) Sampling
a) Populations, samples, random sampling
b) Error associated with sampling
c) Confidence intervals
- 11) Hypothesis formulation
- 12) Analysis of variance
a) T-test
b) Chi-squared
c) F statistics
d) Linear regression
e) Significance testing
- 13) Simple Regression Analysis and Correlation Analysis
- The laboratory experience will emphasize
1. Learning the basics of R
2. Proper data handling, including outliers, summary, and display
3. Discrete distributions beyond the binomial distribution-
especially the Poisson distribution
4. Continuous distributions beyond the normal distribution-
especially the lognormal and exponential distributions
5. Testing of assumptions will be emphasized throughout the
lecture and lab
6. Graphical displays and computations of confidence intervals
7. Graphical displays and computations of hypothesis tests
8. Regression analysis and correlation with emphasis on testing
assumptions
9. Simulations
