Math

Probability and Statics

• Covariance and Correlation

  Definitions, examples, properties, and the relationship between covariance, independence, and correlation.

• Convolution

  A detailed guide to discrete and continuous convolution, including proofs, examples, and graphical calculations.

• Cumulative Distribution Functions and Normal Random Variables

  Understand CDFs for discrete and continuous random variables, normal distributions, standardization, and probability calculations using the standard normal table.

• Continuous Random Variables and Their Distributions

  Learn about continuous random variables, probability density functions, expectation, variance, exponential distributions, and worked examples.

• Decision Trees

  Learn decision trees, entropy, conditional entropy, information gain, and random forests, with formulas and worked examples.

• Independence of Random Variables

  Learn how to check independence and compute the expectation and variance of independent random variables through worked examples.

• Conditional PMFs and the Law of Total Expectation

  Learn how to condition probability mass functions, derive joint and marginal PMFs, and apply conditional expectation and the law of total expectation.

• Joint Probability Mass Functions

  Learn expectations and variances of standard random variables, joint and marginal probability mass functions, marginalization, and functions of multiple random variables.

• Functions of a Random Variable

  Learn how to derive probability mass functions and calculate expectation and variance for functions of random variables.