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  2. MAT1 MATHEMATICAL TRIPOS Part IB Thursday, 08 June, 2023 ...

    https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/paperib_3_2023.pdf
    7 Jul 2023: 18H Statistics(a) Define a uniformly most powerful (UMP) test when X f(|θ) for θ Θ, and. ... ii) Prove that the test in part (i) is UMP of size α for testing H0 : θ 6 0versus H1 : θ > 0.
  3. MAT1 MATHEMATICAL TRIPOS Part IB Tuesday, 06 June, 2023 ...

    https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/paperib_1_2023.pdf
    7 Jul 2023: 6H Statistics(a) Define the generalized likelihood ratio test statistic and state Wilks’ Theorem. ... What isan appropriate statistic and what is the critical region for a test of size α?
  4. MAMA/116, NST3AS/116, MAAS/116 MAT3 MATHEMATICAL TRIPOS Part III…

    https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2023/Paper_116.pdf
    12 Jul 2023: Justify your claims for all parts of the question. [You may use the Tarski-Vaught test for elementarity without proof.
  5. MAMA/218, NST3AS/218, MAAS/218 MAT3 MATHEMATICAL TRIPOS Part III…

    https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2023/Paper_218.pdf
    12 Jul 2023: Give an interpretation of the estimated gender coefficient. The researcher then performed a statistical test and fitted a second model. > ... 3. (b) Explain the statistical test performed by the researcher. State the phenomenonbehind the researcher’s
  6. Contents Units Introduction 1 Numerical Methods 1.1 Fourier…

    https://www.maths.cam.ac.uk/undergrad/catam/II/IIcontents.pdf
    31 Jul 2023: 15 Number Theory. 15.1 Primality Tests 9. 15.10 The Continued Fraction Method for Factorisation 8.
  7. MAMA/107, NST3AS/107, MAAS/107 MAT3 MATHEMATICAL TRIPOS Part III…

    https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2023/Paper_107.pdf
    12 Jul 2023: i) By constructing a suitable test function, prove that weak solutions of (1)satisfy.
  8. MATHEMATICAL TRIPOS Part IA 2023 List of Courses Analysis ...

    https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2023/list_ia.pdf
    7 Jul 2023: Justify your answers. Paper 1, Section I. 4E AnalysisState the comparison test. ... Show that limnPn/Nn = 1. State the alternating series test.
  9. Statistical Learning in Practice (L24) Dr R. Altmeyer Statistical ...

    https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Statistics/Stats_Learning_Practice_Altmeyer.pdf
    21 Feb 2024: Principal component analysis. • Introduction to time series. Prerequisites. Elementary probability theory, maximum likelihood estimation, hypothesis tests and confidenceintervals, linear models.
  10. Advanced Stellar Evolution (L16) Non-Examinable (Graduate Level) Dr…

    https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Astrophysics/Advanced_Stellar_Evolution_Zytkow.pdf
    21 Feb 2024: Theonly way in which we may test stellar structure and evolution theory is through the comparisonof theoretical results to observations.
  11. Planetary System Dynamics (M24) Professor M. Wyatt This course ...

    https://www.maths.cam.ac.uk/postgrad/part-iii/files/GtC/Astrophysics/Planetary_System_Dynamics_Wyatt.pdf
    21 Feb 2024: Secular perturbations: Laplace coefficients, Laplace-Lagrange theory, test particles, secu-lar resonances, Kozai cycles, hierarchical systems. •

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