Introduction to Probability and Statistics
Course facts
- Payment: Free, no certificate
- Credits: Non Credit
- Learning style: Self-paced, start anytime
- Resources: Activity Assignments with Examples; Exam Solutions; Exams; Instructor Insights; Lecture Notes; Problem Set Solutions; Problem Sets; Readings; Supplemental Exam Materials
- Before you start: 18.02 Multivariable Calculus
MIT OpenCourseWare details
- As taught in: Spring 2022
- Department: Mathematics
| Course Details | ||||||
|---|---|---|---|---|---|---|
|
||||||
| Outcomes | ||||||
|
||||||
| Price & Terms | ||||||
|
||||||
| Technical | ||||||
|
||||||
| Specification | ||||||
|
||||||
Probability and statistics with applications: random variables, distributions, Bayesian inference, hypothesis tests, confidence intervals, and regression.
Probability gives the language for uncertainty and statistics the tools to learn from data, and this course teaches both side by side with applications. Classes alternate with hands-on studio sessions in R, working through counting and probability basics, random variables and distributions, the central limit theorem, Bayesian updating, significance testing, confidence intervals and the bootstrap, and linear regression.
What You Will Achieve
- Compute probabilities with counting, conditional probability, and Bayes’ theorem
- Work with discrete and continuous random variables, expectation, and variance
- Update beliefs with Bayesian inference using discrete and continuous priors
- Run significance tests, build confidence intervals, and fit a linear regression
Program Overview
Probability
Counting, chance, and random variables.
- Counting and probability basics
- Conditional probability, independence, and Bayes’ theorem
- Discrete and continuous random variables
- The law of large numbers, the central limit theorem, and joint distributions
Bayesian Statistics
Learning from data by updating beliefs.
- Likelihood and maximum likelihood estimates
- Bayesian updating with discrete and continuous priors
- Beta distributions and conjugate priors
- Choosing priors and probability intervals
Frequentist Statistics and Regression
Testing hypotheses and estimating with confidence.
- Significance testing with z-tests, t-tests, chi square, and ANOVA
- Comparing Bayesian and frequentist approaches
- Confidence intervals and bootstrap confidence intervals
- Linear and multiple regression
Course Completion
Job Outlook
Probability and statistics are used in data science, research in every science, finance and insurance, engineering, public health and any role that draws conclusions from data.
Good for: Learners who want a solid, applied first course in probability and statistics, with both Bayesian and frequentist methods.
Keep in mind: Some problem sets and studios use R and RStudio, so plan to install them; interactive problem checkers live on a separate platform you may enroll in.
Bottom line: A complete probability and statistics course with readings, eleven problem sets and exams, all with solutions.
Frequently Asked Questions
Does the course teach both Bayesian and frequentist statistics?
Yes. It covers Bayesian updating with discrete and continuous priors, then significance testing and confidence intervals, and has a class that compares the two approaches.
Is programming involved?
Some problem sets and the studio sessions use R code and RStudio, with information, tutorials and sample code provided in the course materials.
How can I check my answers?
Solutions are published for all eleven problem sets and the exams, and an interactive problem checker for most sets is linked on the Open Learning Library.
User Reviews
Write your review
You must be logged in to post a review.
Reviews can only be posted by registered learners. Log in or create a free account, then you will return here to post.
There are no reviews yet.