This repository is a collection of course notes and discussion notes for
Math 11 - Calculus-based Introduction to Probability and Statisticsat UCSD, which I prepared while TA-ing during Winter '20 and Spring '20.
Events and probabilities, conditional probability, Bayes’ formula. Discrete and continuous random variables: mean, variance; binomial, Poisson distributions, normal, uniform, exponential distributions, central limit theorem. Sample statistics, confidence intervals, hypothesis testing, regression. Applications. Introduction to software for probabilistic and statistical analysis. Emphasis on connections between probability and statistics, numerical results of real data, and techniques of data analysis.
This course is especially designed for students who are biology-related majors, such as biology, general biology, public health majors, etc, the majority of whom will go on to medical and pharmaceutical schools. That said, a key difference compared to my previous experience is that they do not necessarily have as strong of a background in abstact thinking and mathematical maturity as students majoring in math and engineering related majors.
As such, different from other more traditional probability and statistics classes, I have been trying hard to convey the concepts into "more accessible" language (ie. without using math jargons, such as
instead of "the probability of A conditioned on B", it is now "let's say B has happened, think about how it influences the chance of A happening"
instead of "the probability of the complement of A or B", it is now, "let's say we do not want A to happen, and also B to not happen, what is the probability of that?")
In order to better illustrate concepts, I have had to think of relatable examples, such as
San Diego and California in general are known to have some of the best weather in the country. Say I want to go to the beach tomorrow, what is the chance that I will have to cancel the plan because of rain?
Have you ever wondered how long a green light at a crossing on 1st street in downtown San Diego is?
As such, it has been a fun journey having to juggle between the world of abstract math and the world of everyday life and finding the connections.
The main topics we covered were:
- Descriptive statistics
- Data visualization
- Linear regression: model building and model evaluation
- Basic of probability: axioms, rules, and random variables
- Discrete and continuous distributions
- Further topics in probability
- Statistical inference Central Limit Theorem, condience interval
- Review of probability and statistical inference
- Hypothesis testing: 1-sample and 2-sample tests
- Regression inference, Chi-squared tests Goodness-of-fit test, Independence test
Additionally, to better help students with
- understanding the big picture (ie. the motivation behind each concepts),
- summarizing the key concepts definitions and their formulas,
- comparing and contrasting between similar concepts, and
- giving illustrations and important remakrs,
I prepared this course notes, which acted as a reference guide to all the major concepts covered in the course.
Evaluations from both the instructor, Professor Benjamin Ciotti, and the students are available upon request.