STAT 340

Transformations

Determine the distribution of transformations of random variables (including χ², t, and F) to make the lineage of familiar tools explicit and to practice extending what we know to new problems.

Sampling Distributions

Explore the sampling distributions for sample means and totals from common families.

Convergence

Apply convergence in probability and distribution to prove the Law of Large Numbers and participate in proving the Central Limit Theorems for means and proportions, building confidence with abstraction.

Sufficiency

Find sufficient statistics in one-parameter models using the factorization theorem in order to justify responsible data reduction.

Point Estimation

Derive method-of-moments, maximum-likelihood, and Bayesian estimators to show that familiar estimators rest on principled foundations.

Interval Estimation

Construct confidence intervals via pivots and Bayesian credible intervals to communicate uncertainty honestly so stakeholders can make informed decisions.

Hypothesis Testing

Apply the Neyman–Pearson lemma to find most-powerful tests for problems involving simple hypotheses.

Evaluation

Assess estimators by bias, variance, and MSE; practice acknowledging trade-offs.

Simulation

Examine sampling distributions and evaluate estimators using simulation to make uncertainty visible, sharpen intuition, and introduce another way to approach problem solving.

Critical Thinking

Strengthen problem-solving and reasoning, building confidence to tackle unfamiliar problems and act responsibly under uncertainty.

Collaborative Problem Solving

Solve problems in teams by listening well, giving and receiving help, and practicing mutual respect and accountability.

Ethical Gen-AI Stewardship

Engage generative-AI tools as study partners by crafting purposeful prompts, verifying and citing AI contributions, and discerning when to rely on human reasoning---recognizing that AI is neither divine nor human and cannot love, covenant, or receive revelation.