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Continuous models and inference extension

This required extension follows concepts 1–15 and CAL1–CAL6 in Calculus Foundations. It adds 25–35 focused hours: lessons and written practice 12–16, executable lab and memo 8–12, assessment and delayed repair 5–7. These author estimates await learner calibration. The probability module total becomes 70–100 hours; calculus study is counted separately in the semester.

Study sequence​

  1. Transformations and inverse sampling.
  2. Joint and conditional densities.
  3. Likelihood estimation.
  4. Bayesian parameter updates.
  5. Exact paired randomization.

Complete each lesson’s check and drill, then the practice set, lab and assessment. General multivariable transformations, asymptotic likelihood theory, bootstrap confidence intervals, regression, power analysis and sequential tests remain later extensions. They are not implied by passing these gates.

Sources and selective reading​

Use the local lessons as the main teacher; full-book reading is not required. The original module’s book backbone remains useful for distributions and conditioning. Free primary support:

  • Pishro-Nik: transformations: follow the CDF method, then derive the local power transformation and inverse-sampling rule.
  • Pishro-Nik: joint densities: follow one normalization and marginalization example, then solve the local triangular-support task unaided.
  • Pishro-Nik: maximum likelihood: contrast parameter and observation roles, then derive the exponential estimator and its boundary failure yourself.
  • Pishro-Nik: Bayesian inference: read the setup; follow the next sections for posterior normalization if needed. Derive the local Beta update by multiplying kernels.
  • SciPy permutation-test documentation: read the paired samples design and exact-enumeration discussion. Compare its tail convention with the locally specified absolute-sum convention; installing SciPy is not required.

These topic readings and the local written practice are included in the estimate. Additional full courses are optional. Resources were checked on 2026-10-22. No purchase or book conversion is needed.