PSTAT 120A

Welcome to CLAS / PSTAT 120A Study Page!

We have uploaded by-topic notes on various topics of PSTAT 120A, including 88 practice problems, each with detailed solutions. We also have 5 practice midterms and 7 practice finals to help you prepare for exams! Please come to CLAS weekly group session and drop-in office hours if you have any questions.

1: Set Theory / Calculus Review 

Topics: 

1. Basic Set Theory: union/intersection/complement, countable vs. uncountable, De Morgan's law, partition, ...

2. Calculus Review: function basics, derivatives and integrals, geometric series, Taylor series expansion, ...

Calculus Review Practice Problem: 1.1 ~ 1.14

2: Axioms of Probability

Topics: Three axioms of probability and consequences of the axioms: monotonicity, complement, law of total probability, ...

Axioms of Probability Practice Problem: 2.1 ~ 2.10

3: Conditional Probability

Topics: Conditional Probability, Bayes' Rule, Independence and Conditional Independence of Events, ...

Conditional, Bayes, Independence Practice Problem: 3.1 ~ 3.13

4: Random Variables

Topics: 

1. Random variables: Cumulative distribution functions. Probability mass functions (PMF) for discrete random variables. Probability density functions (PDF) for continuous random variables.

2. Named discrete random variables: Bernoulli, Binomial, Geometric, Hypergeometric, Poisson

Random Variables, PMF/PDF/CDF Practice Problems: 4.1 ~ 4.12

Named Discrete Random Variables Practice Problems: 5.1 ~ 5.7

5: Expected Value and Variance

Topics:

1. Expected value: Expectation of a function of random variables, linearity of expectation, moments, ...

2. Variance: definition and properties.

Expected Value and Variance Practice Problems: 6.1 ~ 6.8

Videos on Named Random Variables

6: Moment Generating Functions; Exponential & Normal Distributions

Topics: Moment Generating Functions, Exponential distribution, Normal distribution

Moment Generating Functions Practice Problems: 7.1 ~ 7.6

7: Transformation of Random Variables

Topics: CDF method, Change of Variable Formula, MGF method

8: Joint/Conditional Distribution, Covariance

Topics: Joint distribution of two discrete and continuous random variables. Joint CDF. Expected value of a function of a bivariate random vector. Conditional distribution and conditional expectation. Covariance and correlation.

Joint/Conditional Distribution, Covariance Practice Problems: 8.1 ~ 8.18

9: Limit Theorems

Topics: Markov's Inequality, Chebychev's Inequality, Weak Law of Large Numbers, Central Limit Theorem, Convergence of Random Variables

Practice Finals

Good luck with your finals!

Videos - Extending 120A to 120B

UCSB CLAS ECON & STATS