Probability & Statistics

Types of data, graphical displays, measures of center and spread, five-number summary, and the empirical rule.

Sample spaces, counting techniques, probability rules, conditional probability, Bayes theorem, and study design.

Random variables, expected value, binomial, geometric, Poisson, and hypergeometric distributions.

PDFs, CDFs, uniform, normal, exponential, Weibull, t, chi-squared, and F distributions.

Sampling distributions of means and proportions, properties of estimators, and sample size determination.

Confidence intervals for means and proportions, margin of error, prediction and tolerance intervals.

Testing framework, tests for means and proportions, Type I/II errors, power, and effect size.

Goodness-of-fit tests, independence and homogeneity tests, correlation, and R-squared.

One-way and two-way ANOVA, multiple comparisons, factorial designs, and response surface methodology.

Simple and multiple linear regression, inference on slope, prediction intervals, and model selection.

Statistical process control, control charts, process capability, reliability functions, and system reliability.

Bayesian inference, conjugate priors, nonparametric tests, bootstrap resampling, and maximum likelihood estimation.

Simpson's paradox, survivorship bias, regression to the mean, p-hacking, and other reasoning traps that affect real-world data analysis.

Study design taxonomy, effect measures (RR, OR, NNT), survival analysis, clinical trials, and meta-analysis for health sciences and bioengineering.