An introduction to statistics and probability covering essential topics. Sample space, discrete and continuous random variables, probability distributions, joint and conditional distributions, expectation, transformation of random variables, limit theorems, estimation theory, hypothesis testing, confidence interval, statistical tests, and regression.
Course Lead/Main Instructor
The aim of this course is to introduce concepts of Probability and Statistics.
- Apply key concepts of probability, including discrete and continuous random variables, probability distributions, conditioning, independence, expectations, and moments
- Define and explain the different statistical distributions (e.g., normal, log-normal, Poisson) and the typical phenomena that each distribution often describes
- Apply the basic rules and theorems in probability including Bayes’s theorem and the Central Limit Theorem (CLT)
- Define and demonstrate the concepts of estimation and properties of estimators
- Apply the concepts of interval estimation and confidence intervals
- Apply the concepts of hypothesis testing and p-value
- Apply the method of least squares to estimate the parameters in a regression model
- Use software to facilitate statistical analysis
- Evaluate the probabilities and conditional probabilities
- Evaluate expectations and conditional expectations of random variables
- Approximate the distribution of sum of random variables using CLT
- Construct point estimators using the method of maximum likelihood
- Calculate the number of samples needed to construct confidence levels on the mean and variance of a normal distribution
- Design hypothesis tests for a given set of data and select the appropriate thresholds for the tests
- Use linear regression analysis to develop an empirical model of experimental data.
- Apply computer programs to facilitate the analysis of data.
- Cohort based lecture
- Hands-on projects
Text & References
- Essentials of Probability and Statistics for Engineers and Scientists, by R. Walpole. et al.
- Class participation: 5%
- Homework: 25%
- Project: 10%
- Mid-term exam: 30%
- Final exam: 30%
Homework is assigned on every week and is due in the 1st class of the following week.