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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.


Lecture Topic
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.


Note: some of these resources cover much more material than DSCI 551.

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