# ENGRCEE 11 Methods II: Probability and Statistics (2015-2016)

#### ENGRCEE 11 Methods II: Probability and Statistics

**ENGRCEE 11 Methods II: Probability and Statistics (Credit Units: 4)** Modeling and analysis of engineering problems under uncertainty. Engineering applications of probability and statistical concepts and methods. Prerequisite: EECS 10, EECS 12, CEE 20, MAE 10, or CSE 41/I&C SCI 31; Mathematics 3A. Civil Engineering and Environmental Engineering majors have first consideration for enrollment. (Design units: 0)

1. Understand the concepts of probability and statistics. (EAC a, EAC k)

2. Acquire basic knowledge of fundamental probability distribution functions, discrete and continuous, uni-variate and multi-variate. (EAC a)

3. Estimate and interpret correlation coefficient. (EAC a)

4. Carry out point and interval estimations involving normal populations. (EAC a)

5. Understand hypothesis testing and the meaning of the null hypothesis. (EAC a, EAC e)

6. Have an appreciation for Monte Carlo simulation techniques. (EAC a, EAC e, EAC k)

- Basic computer skills and programming skills.
- Basic Calculus and Linear Algebra

- Introduction and Descriptive Statistics (1 week) – Overview of probability and statistics, Pictorial and tabular methods in descriptive statistics, Measures of location, Measures of variability
- Introduction to Probability (1 week) – Sample spaces and events, Axioms, Interpretations and properties of probability, Conditional probability, Bayes’ Theorem, Independence
- Counting techniques (1 week) – Permutations and combinations
- Discrete Random Variables and Probability Distributions (2 weeks) – Random variables, Probability distributions for discrete random variables, Expected values of discrete random variables, The Binomial distribution, The Poisson distribution
- Continuous Random Variables (1 week) – Continuous random variables and probability density functions, Distribution functions and expected values, The Normal distribution, The exponential distribution
- Joint Probability Distributions and Random Variables (1 week) – Jointly distributed random variables, Expected values, covariance and correlation, The distribution sample means, The Central Limit Theorem, distribution of a linear combination.
- Point estimation (1 week) – Unbiasedness, methods of point estimation
- Confidence Intervals (1 week) – Confidence interval of sample means
- Test of hypotheses based on a single sample (1 week) – Hypotheses and test procedures, Tests about a population mean
- Monte Carlo simulation (1 week)

Meets for 3 hours of lecture and 1 hour of discussion each week for 10 weeks.

- Use of spreadsheet and statistical software
- Use of online reading materials and class notes
- Online quizzes

Design of statistical tests for inferences and selection of such test procedures.

Contributes to the Math and Basic Science courses of Civil Engineering and Environmental Engineering majors.

- Class Participation/Quizzes: 15%
- Homework: 15%
- Midterm Exam: 30%
- Final Exam: 40%
- Total: 100%

Mathematics and Basic Science: 4.0 credit units

Computing: 0.0 credit units

Engineering Topics: 0.0 credit units

Engineering Science: 0.0 credit units

Engineering Design: 0.0 credit units