Ditributions and their stories

Uniform Distribution and the Probability Integral Transform

Moment Generating Functions (MGF)

Probability Generating Functions (PGF)

Multivariate Gaussian Distribution

Multivariate Gaussian Distribution: Random Sampling and the Cholesky

One-Sample Mean compared to Population & Confidence Intervals

Independent Samples Means Test

Confidence Interval and Margin of Error

Comparing Sample Proportion to Population: Z-test proportions, CI and margin of error

Comparing Sample Proportions to Population: Exact Multinomial (Goodness of Fit)

Comparing Sample Proportions: Fisher Exact; Chi square; G-test; Z-test

Chi Square: Test of Independence and Homogeneity

Chi Square: Testing Standard Deviation (Variance)

Chi Square Test in R: Monte Carlo Option

Grading on the curve: detectable with GoF test

Monte Carlo Validation of the Z Test of Proportions

Monte Carlo alternative to Chi Square

Global and individual predictors p-values of explained variance in a linear model

Variance-Covariance Matrix and A transpose A

Calculating Sts. Error, t value and Pr(>|t|) of coefficients

Manual calculation ANOVA OLS lm Models

Confidence Intervals & p-values of OLS

Interpretation of Output in Linear Model with Interactions

Comparing Models with Mixed Effects

Predict Function in Mixed Effects

Model Matrices in Mixed Effects

Confounders, Control Variables, Endogeneity

On the meaning of Parametric v Nonparametric

Random walk - Return to origin

Time Series: Variance, Covariance and Correlation

Alternate formula variance (raw moments)

Convolution or pdf of Z = X + Y

Simpson's Paradox and Random Effects

Natural phenomena are not Gaussian

A Practical Example of Markov Chain Monte Carlo (MCMC)

Systems of linear equations and basis for the four spaces