Search

21 Jul 2022: Logic. The following multiple choice self-test questions are intended to give an indication whether you haveprerequisites for the Part III courses in logic.

3 Aug 2022: Suppose thereexists a likelihood ratio test of size α for H0 against H1. ... Specify the test statistic and thecritical region. Is this test uniformly most powerful for the alternative H1 : π > 0?

21 Jul 2022: Set Theory. The following multiple choice self-test questions are intended to give an indication whether you haveprerequisites for the Part III courses in set theory.

17 Mar 2022: To test this enter. >> amatrix=printsquares(1,10);. >> amatrix. Note that we have used amatrix as the name of the matrix in which to store the output fromthe function printsquares; we ... 4.4 Exercises. 1. Test your function printsquares with m60 and m>n,

4 Aug 2022: a) Let Tn =1n. ni=1(θ1 θ0). (xi θ0θ12. ). Show that a likelihood ratio test should. ... Assuming thisfact, show that a hypothesis test based on Sn corresponds to a likelihood ratiotest of.

3 Aug 2022: Part IA, Paper 1. 3. 3D Analysis IState the alternating series test. ... You may use the comparison test, provided that you accurately state it.].

4 Aug 2022: Explainwhy a test for the hypothesis of part (a) based on the first K eigenfunctions ofC, as defined in part (b), might be preferable to a test based on the first ... Define a finite-dimensional statistic, based on the first K eigenfunctions of

3 Aug 2022: d) Describe a test of size α for the null hypothesis H0 : σ21 = σ. ... Suppose thereexists a likelihood ratio test of size α for H0 against H1.

4 Aug 2022: Show that the smallest. possible total error probability that can be achieved by any hypothesis test is equalto:. ... b) Consider a simple-versus-simple hypothesis test between two distributions P andQ 6= P having full support on a finite alphabet A.

3 Aug 2022: d) Describe a test of size α for the null hypothesis H0 : σ21 = σ. ... 22 against the. alternative H1 : σ21 < σ. 22, using the test statistic.

4 Aug 2022: observations (xi,yi,zi) R R Rp for i = 1,. ,n. We wish to test the null hypothesis H0: x1 y1 |z1. ... Give a choice of s (depending on h) such that wecan expect the resulting test will have power against this alternative.

4 Aug 2022: Is the test valid?What can we conclude from this test? > 1-pchisq((21.061-18.185)/0.31,df=3, lower.tail=TRUE). ... d) The research team wants to use a statistical test to see if lme1 or lme2 fitsthe data better.

28 Apr 2022: covering definitions, theorems, proofs, standard techniques, applications and examples). (b) Work through a good number of past exam questions to (i) test and improve your knowledge and. ... Examiners set questions that. test as much of the course as is

3 Aug 2022: 2. Paper 1, Section I3D Analysis I. State the alternating series test. ... You may use the comparison test, provided that you accurately state it.].

4 Aug 2022: andCx,Ht = X. x,Ht Ht1 Pt. for x R and n-dimensional previsible process H.(a) Briefly explain the economic interpretation of the processes Xx,H and Cx,H.

4 Aug 2022: 8. 4 Analysis of Survival DataDerive the log-rank test for comparing two time-to-event distributions.

4 Aug 2022: Show that theexpectation value 〈p2〉 does immediately change. Explain what type of tests of the GRWmodel this suggests.

27 Jan 2022: MATHEMATICAL TRIPOS Part II 2021. List of Courses. Algebraic Geometry. Algebraic Topology. Analysis of Functions. Applications of Quantum Mechanics. Applied Probability. Asymptotic Methods. Automata and Formal Languages. Classical Dynamics. Coding

4 Aug 2022: Describe, in detail, a randomiza-tion test for the sharp null hypothesis that A has no effect on Y and prove that itcontrols the type I error rate.

4 Aug 2022: ω|2 = G(M1 M2)R3. Let us consider the equilibrium points of a test particle S belonging to subhalo H2.Let us introduce Cartesian (x,y,z) with origin at

12 Jan 2022: MATHEMATICAL TRIPOS Part II 2020. List of Courses. Algebraic Geometry. Algebraic Topology. Analysis of Functions. Applications of Quantum Mechanics. Applied Probability. Asymptotic Methods. Automata and Formal Languages. Classical Dynamics. Coding