DSCI 551: Descriptive Statistics and Probability for Data Science
Fundamental concepts in probability. Describing data generated from a probability distribution. Statistical view of data coming from a probability distribution.
|1||Probability intro/review: Boolean algebra / logic / Venn diagram with events and probabilities, random variables, transformations of variables, probability distributions (pmf & cdf) for discrete random variables. Properties of a distribution: mean, median, mode, variance, entropy. Linearity of expectations.|
|2||Well-known discrete distributions. Conditional probabilities (univariate).|
|3||Bayes' Theorem. Multivariate distributions (discrete): joint, marginal, conditional, covariance. (in)dependence. Variance of a sum.|
|4||Continuous random variables and their distributions (univariate); CDF vs PDF. Quantiles. Support.|
|5||Finding expected values and functions of expected values with continuous distributions. Multivariate continuous distributions as distributions over vectors. Covariance, correlation, etc.|
|6||Review of vectors and linear algebra. Multivariate Gaussian distribution.|
|7||Mixtures of (univariate/multivariate) Gaussians. View of data as coming from a probability distribution. Setting the stage for supervised learning: response variables, predictors, conditioning on predictors, and more.|
|8||Various topics related to what we've done in the course; an intro to maximum likelihood estimation.|
- JBstatistics (also on YouTube)
- Seeing Theory
- Introduction to Probability, Statistics, and Random Processes
- Harvard STAT 110 course plus YouTube videos
- Probability Cheatsheet and another one
Note: some of these resources cover much more material than DSCI 551.