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Probability

Free Probability study guide: 10 units with summaries, key ideas, flashcards and 300 practice questions with step-by-step solutions.

Lines up with: College probability course; actuarial Exam P basics.

Units

1. UNIT 01

   Counting and Combinatorics

   Counting methods let you find the size of a sample space and of events without listing outcomes. Classical probability, poker hands and many exam problems depend on counting correctly.
2. UNIT 02

   Axioms of Probability

   Probability is built on a sample space of outcomes, events that are subsets of it, and three axioms. Every rule you use later, from the complement rule to inclusion–exclusion, follows from these axioms.
3. UNIT 03

   Conditional Probability and Bayes' Theorem

   Conditional probability measures how likely an event is once you know another event happened. Bayes' theorem and the law of total probability are among the most tested ideas in any probability course.
4. UNIT 04

   Discrete Random Variables

   A random variable assigns a number to each outcome of an experiment. This unit covers how discrete random variables are described by PMFs and CDFs and summarized by expected value and variance.
5. UNIT 05

   Binomial, Geometric and Poisson Distributions

   A few named discrete distributions model most counting situations: successes in fixed trials, waiting times, and rare events. Knowing their PMFs, means and variances, and when each applies, is essential for every probability exam.
6. UNIT 06

   Continuous Random Variables

   Continuous random variables take values in intervals, and their probabilities are areas under a density curve. This unit replaces sums with integrals and adds tools such as percentiles and transformations.
7. UNIT 07

   Normal, Exponential and Uniform Distributions

   The uniform, exponential and normal distributions are the core continuous models, with the gamma as a natural extension. This unit covers their formulas, key properties and the normal approximation to the binomial.
8. UNIT 08

   Joint Distributions and Independence

   Joint distributions describe two or more random variables together. You will find marginals and conditionals, test independence, and compute probabilities over regions, which is where many exam problems become double integrals.
9. UNIT 09

   Expectation, Variance and Covariance

   This unit extends expectation and variance to several random variables. Covariance, conditional expectation and moment generating functions are the tools behind portfolio risk, compound claims and most limit theorems.
10. UNIT 10

    Limit Theorems (LLN, CLT)

    Limit theorems describe what happens when many independent random variables are added or averaged. The law of large numbers explains why averages settle down, and the central limit theorem lets you approximate sums with the normal distribution.