BCS Written Statistics study plan

Derive and state the axioms of probability, then compute probabilities for unions, intersections, and complements of events in five constructed scenarios

Apply Bayes' theorem to solve at least six two-stage conditional probability problems and interpret each posterior in plain language

Distinguish discrete from continuous random variables and derive the mean and variance of the binomial, Poisson, and geometric distributions from their probability mass functions

Produce a one-page formula sheet linking expectation, variance, and moment generating functions for the named distributions

Derive the probability density functions, means, and variances of the normal, exponential, and gamma distributions and sketch each curve

Apply the central limit theorem to approximate sampling distributions in at least four worked problems

Define estimator properties (unbiasedness, consistency, efficiency, sufficiency) and test each property for the sample mean and sample variance

Solve for maximum likelihood estimators in three standard models and verify second-order conditions

Construct confidence intervals for means, proportions, and variances under both known and unknown population variance, and state the assumptions behind each interval

Formulate null and alternative hypotheses for ten applied scenarios and identify the correct test statistic and reference distribution

Compute and interpret Type I error, Type II error, and power for a one-sample z-test at three effect sizes

Execute and interpret likelihood ratio tests for two nested models

Design a completely randomized experiment and a randomized complete block design for two stated research questions, justifying the choice

Derive the ANOVA decomposition of total sum of squares for one-way classification and construct the full ANOVA table

Check ANOVA assumptions using residual plots and describe two remedies when assumptions fail

Perform and interpret post-hoc pairwise comparisons with an appropriate multiple-comparison adjustment

Extend ANOVA to two-factor designs with and without interaction and interpret each F-ratio

Distinguish simple random, stratified, systematic, and cluster sampling by design, estimator, and variance formula

Compute sample size requirements for estimating a population mean and proportion under specified precision and confidence

Derive the ratio estimator and explain when it outperforms the expansion estimator

Analyze the effects of nonresponse and coverage error on survey estimates and propose two mitigation strategies

Fit a multiple linear regression model, interpret coefficients, and test individual and joint significance

Diagnose multicollinearity, heteroscedasticity, and influential observations and state corrective actions

Explain the purpose of principal component analysis and interpret a small worked example

Decompose a time series into trend, seasonal, and irregular components and compute a moving-average trend estimate

Fit and interpret an ARIMA model, including using autocorrelation and partial autocorrelation plots to choose orders

Produce and evaluate a short-term forecast with at least one accuracy measure

Define and compute crude and age-specific death rates, standardized mortality ratios, and life-table quantities

Implement probability calculations, a hypothesis test, and a one-way ANOVA in a statistical software environment and document the code

Reproduce three earlier manual calculations in software and reconcile any discrepancies

Complete a timed full-length mock examination under exam conditions and self-mark against the syllabus

Compile a prioritized revision list of the five weakest topics identified by the mock