Probability and Statistics 0.2.1

Learning outcomes

1. Construct probability models, compute conditional/Bayesian probabilities, and assess independence assumptions.
2. Compute with discrete and continuous random variables, common distributions, expectation, variance, and transformations.
3. Analyse joint behaviour, covariance/correlation, sums, LLN, CLT, and Monte Carlo estimates.
4. Distinguish populations, samples, statistics, bias, measurement error, exploratory summaries, and sampling distributions.
5. Evaluate estimators by bias/variance/MSE and construct/interpet confidence intervals and likelihoods.
6. Perform hypothesis tests while interpreting p-values, power, multiplicity, effect size, and practical significance correctly.
7. Fit and diagnose simple linear regressions and quantify mean-response versus new-observation prediction uncertainty.
8. Design defensible analyses, test robustness, and communicate statistical uncertainty without overclaiming.