Statistics and Probability for Data Science

DS14270: deck-aligned mathematics followed by executable R.

Author

Samer El Kababji

SD01 — Statistical Thinking

Source deck: Samer El Kababji, SD01 — Statistical Thinking. These companions turn applicable ideas into mathematics followed immediately by R code. Simulations extend the concepts and are labeled as fictional. The four displayed loan records are transcribed from the deck.

Companion	Focus
SD01-01: Data Matrices and Variables	Rows, columns, variable types, and shared-cause association
SD01-02: Covariates, Confounding, Association, and Causation	Group comparisons without regression
SD01-03: Populations and Sampling	Simple, stratified, cluster, multistage, and convenience samples

SD02 — Exploratory Data Analysis

Source deck: Samer El Kababji, SD02 — Exploratory Data Analysis.

Companion	Focus
SD02-01: Descriptive Statistics and Quantiles	Mean, variance, proportion, median, and linearly interpolated quartiles
SD02-02: Shape and Univariate Plots	Dot plots, histograms, skewness, kurtosis, modes, and box plots
SD02-03: Comparing Variables with Plots	Scatter plots, categorical bar plots, grouped box plots, and violin plots

SD03a — Probabilities

Source deck: Samer El Kababji, SD03a — Probabilities.

Companion	Focus
SD03a-01: Sample Spaces, Events, and Probability Rules	Outcomes, events, complements, set operations, axioms, and addition rules
SD03a-02: Conditional Probability, Bayes’ Theorem, and Independence	Conditioning, total probability, Bayes updates, and independent events
SD03a-03: Bayes Decision Rules and Naïve Bayes	Prior, likelihood, posterior, ML and MAP rules, and binary naïve Bayes

SD04 — Random Variables

Source deck: Samer El Kababji, SD04 — Random Variables.

Companion	Focus
SD04-01: Random Variables, PMFs, PDFs, and CDFs	Discrete and continuous random variables, probability functions, and cumulative distributions
SD04-02: Expectation, Variance, and Quantiles	Moments, standard deviation, percentiles, quartiles, and exponential-distribution calculations
SD04-03: Properties of Expectation, Variance, and Standardization	Linear transformations, sums of variables, covariance terms, and z-scores
SD04-04: Joint Random Variables, Covariance, and Correlation	Joint and marginal PMFs, independence, covariance, and linear correlation

SD05 — Discrete Distributions

Source deck: Samer El Kababji, SD05 — Discrete Distributions.

Companion	Focus
SD05-01: Bernoulli and Binomial Distributions	Bernoulli trials, binomial counts, cumulative probabilities, and moments
SD05-02: The Hypergeometric Distribution	Sampling without replacement, finite-population correction, and binomial approximation
SD05-03: The Negative Binomial Distribution	Failures before a fixed number of successes, counting conventions, and moments
SD05-04: The Poisson Distribution	Event counts, interval scaling, moments, and binomial approximation

SD06 — Continuous Distributions

Source deck: Samer El Kababji, SD06 — Continuous Distributions.

Companion	Focus
SD06-01: Uniform Distribution and Monte Carlo Simulation	Uniform probabilities, moments, random generation, and Monte Carlo estimation
SD06-02: Exponential and Gamma Distributions	Waiting times, survival probabilities, gamma parameterizations, and event processes
SD06-03: Weibull Distribution and Survival	Lifetime probabilities, survival and hazard functions, shape, scale, and moments
SD06-04: Normal Distribution and Z-Scores	Normal probabilities, standardization, empirical rule, quantiles, and linear combinations

SD07 — Sampling Distributions and Inference

Source deck: Samer El Kababji, SD07 — Sampling Distributions and Inference.

Companion	Focus
SD07-01: Sample Means and the Central Limit Theorem	Sampling distributions, standard error, exact normal results, and the CLT
SD07-02: Point Estimation and Sampling Error	Estimators, estimates, sampling error, standard error, unbiasedness, and variance estimation
SD07-03: Confidence Intervals	z and t intervals for means, proportion intervals, margin of error, and coverage
SD07-04: Maximum Likelihood Estimation	Likelihood, log-likelihood, and Poisson and exponential MLE derivations

Run the companions

Open any .Rmd file in RStudio and run its R chunks from top to bottom, or use Knit to create HTML. Every lesson is independent and uses base R. Rendering requires knitr and rmarkdown. From this folder:

Code

rmarkdown::render("SD01-01-data-matrices-and-variables.Rmd")

The separate Advanced Statistical Modeling course contains the existing logistic and mixed-effects regression lessons.