Probability and Distributions for Modeling Data

Apply Bayes' theorem to update beliefs given new evidence in a machine learning context.

Calculate the expected value and variance of random variables to characterize their central tendency and spread.

Model binary outcomes and count data using Bernoulli, Binomial, and Poisson distributions.

Model continuous measurements and waiting times using Normal and Exponential distributions.

Apply the Central Limit Theorem to explain the prevalence of the normal distribution in sample means.

Calculate covariance and correlation to measure the linear relationship between two variables.

Construct and interpret a covariance matrix for a multivariate dataset.

Describe the properties of a Multivariate Normal distribution and its importance in modeling.