Mathematics: Analysis and Approaches HL

Statistics and probability

Higher-level probability reasoning, Bayes theorem, and continuous random variables.

Apply Bayes theorem to three sources Develop apply bayes theorem to three sources through finite, exact AA HL practice aligned to current syllabus point AHL 4.13. Normalize linear continuous densities Develop normalize linear continuous densities through finite, exact AA HL practice aligned to current syllabus point AHL 4.14. Calculate discrete expectation and variance Develop calculate discrete expectation and variance through finite, exact AA HL practice aligned to current syllabus point AHL 4.14. Calculate probabilities from continuous densities Develop calculate probabilities from continuous densities through finite, exact AA HL practice aligned to current syllabus point AHL 4.14. Find medians of continuous uniform densities Develop find medians of continuous uniform densities through finite, exact AA HL practice aligned to current syllabus point AHL 4.14. Find modes of continuous quadratic densities Develop find modes of continuous quadratic densities through finite, exact AA HL practice aligned to current syllabus point AHL 4.14. Calculate means of continuous triangular densities Develop calculate means of continuous triangular densities through finite, exact AA HL practice aligned to current syllabus point AHL 4.14. Calculate variances of continuous uniform densities Develop calculate variances of continuous uniform densities through finite, exact AA HL practice aligned to current syllabus point AHL 4.14. Transform random-variable means and variances Develop transform random-variable means and variances through finite, exact AA HL practice aligned to current syllabus point AHL 4.14. Standardise normal random variables Develop standardise normal random variables through finite, exact AA HL practice aligned to current syllabus point AHL 4.12. Determine whether probability games are fair Develop determine whether probability games are fair through finite, exact AA HL practice aligned to current syllabus point AHL 4.14. Calculate standard deviations from moments Develop calculate standard deviations from moments through finite, exact AA HL practice aligned to current syllabus point AHL 4.14. Calculate affine expectations from moments Develop calculate affine expectations from moments through finite, checked AA HL practice aligned to current syllabus point AHL 4.14. Normalize piecewise continuous densities Develop normalize piecewise continuous densities through finite, checked AA HL practice aligned to current syllabus point AHL 4.14. Find medians of linear continuous densities Develop find medians of linear continuous densities through finite, checked AA HL practice aligned to current syllabus point AHL 4.14. Transform standard deviations of random variables Develop transform standard deviations of random variables through finite, checked AA HL practice aligned to current syllabus point AHL 4.14. Calculate moments of power densities Develop calculate moments of power densities through finite, checked AA HL practice aligned to current syllabus point AHL 4.14. Recover normal values from z-scores Develop recover normal values from z-scores through finite, checked AA HL practice aligned to current syllabus point AHL 4.12. Apply Bayes theorem with complements Develop apply bayes theorem with complements through finite, checked AA HL practice aligned to current syllabus point AHL 4.13. Calculate expected returns from two-stage games Develop calculate expected returns from two-stage games through finite, checked AA HL practice aligned to current syllabus point AHL 4.14. Transform continuous uniform random variables Develop transform continuous uniform random variables through finite, checked AA HL practice aligned to current syllabus point AHL 4.14. Compare variance after scaling and shifting Develop compare variance after scaling and shifting through finite, checked AA HL practice aligned to current syllabus point AHL 4.14.