Just cause it is boring doesn't mean we shouldn't cover it... I admit my bias freely; statistics is far from my favorite subject. It feels the least *pure* of the subjects I have seen. Perhaps I will feel differently when I am wiser. I will initially be following the Advanced High School Statistics, available for free, and hopefully soon as a PreTeXt book. Maybe afterwards I will read something more rigorous and change things # Data collection # Summarizing data ## Examining numerical data ### Scatterplots for paired data ### Stem-and-leaf plots and dot plots ### Histograms ### Describing Shape ### Descriptive versus inferential statistics ## Numerical summaries and box plots ### Measures of center ### Standard deviation as a measure of spread ### Z-scores ### Box plots and quartiles ### Technology: summarizing 1-variable statistics ### Outliers and robust statistics ### Linear transformations of data ### Comparing numerical data across groups ### Mapping data (special topic) # Probability and probability distributions ## Introduction to Probability ### Basic probability concepts #### The role of probability [[Probability]] provides the theoretical framework for understanding and quantifying randomness and uncertainty, and it is essential for making valid and reliable inferences from data in statistics. #### Terms [[Sample Space]]: The [[set]] of all possible outcomes of a random experiment. [[Event]]: Any [[Subset|subset]] of the [[sample space]]. - [[Simple Event]]: An [[Element of a Set|element]] of the [[Sample Space]] - [[Composite Event]]: A [[subset]] of the [[sample space]] that has more than one [[Element of a Set|element]] [[Probability]]: A measure of the likelihood of an event occurring, expressed as a number between 0 and 1. Certain Event: An event with a probability of 1. Impossible Event: An event with a probability of 0. Mutually Exclusive Events: Events that cannot occur at the same time. Complementary Events: Events that together make up the entire sample space. ### Rules of probability (addition and multiplication) ## Discrete Probability Distributions - Discrete random variables - Probability mass function (PMF) - Cumulative distribution function (CDF) - Common discrete distributions (Bernoulli, binomial, geometric, Poisson) ## Continuous Probability Distributions - Continuous random variables - Probability density function (PDF) - Cumulative distribution function (CDF) - Common continuous distributions (uniform, normal, exponential, etc.) ## Joint and Marginal Probability - Joint probability mass/density function - Marginal probability mass/density function - Conditional probability - Independence and dependence ## Expectation and Variance - Expectation of a random variable - Variance and standard deviation of a random variable - Properties of expectation and variance - Chebyshev's inequality VI. Sampling and Estimation - Point estimation - Interval estimation - Central Limit Theorem - Law of Large Numbers VII. Hypothesis Testing - Null and alternative hypotheses - Test statistics - p-value - Common tests (t-test, chi-squared test, etc.) VIII. Bayesian Inference - Bayes' theorem - Prior and posterior distributions - Conjugate priors - Markov Chain Monte Carlo (MCMC) methods IX. Advanced Topics - Multivariate distributions - Time series analysis - Stochastic processes - Decision theory.