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Mathematical Tripos: Part IB SMP/Lent 2014 Statistics: Example Sheet…
https://www.dpmms.cam.ac.uk/study/IB/Statistics/2013-2014/ex2.pdf12 Feb 2014: Isthe test uniformly most powerful for testing H0 : θ = θ0 against H1 : θ > θ0? ... By first deriving the MLEs under each hypothesis, showthat the likelihood ratio and Pearson’s chi-squared tests are identical to those for theindependence test. -
Mathematical Tripos: Part IB SMP/Lent 2013 Statistics: Example Sheet…
https://www.dpmms.cam.ac.uk/study/IB/Statistics/2012-2013/ex2.pdf18 Feb 2013: Isthe test uniformly most powerful for testing H0 : θ = θ0 against H1 : θ > θ0? ... By first deriving the MLEs under each hypothesis, showthat the likelihood ratio and Pearson’s chi-squared tests are identical to those for theindependence test. -
STATISTICS Part IB Example Sheet 2 (of 3) RJS/Lent ...
https://www.dpmms.cam.ac.uk/study/IB/Statistics/2009-2010/Example2.pdf8 Feb 2010: 6. Write down the model and hypotheses for a test of homogeneity in a two-way contingencytable. ... Show that the likelihood ratio and Pearson’s chi-squared tests are identical to thosefor the independence test. -
ANALYSIS I EXAMPLES 1 G.P. Paternain Lent 2022 Comments ...
https://www.dpmms.cam.ac.uk/study/IA/AnalysisI/2021-2022/aI_1_22.pdf22 Jan 2022: Show also that. n=1(1)n1andiverges. [This shows that, in the alternating series test, it is essential that the moduliof the terms decrease as n increases.]. ... sequence. Prove that. j=1 ajbj converges. Deduce the alternating series test. Does the series. -
ANALYSIS I EXAMPLES 1 G.P. Paternain Lent 2010 Comments ...
https://www.dpmms.cam.ac.uk/study/IA/AnalysisI/2009-2010/aI1.pdf18 Jan 2010: bndivergent. 9. (Abel’s test.) Let an and bn be two sequences and let Sn =n. ... Deduce the alternating series test. Does the series. n=1cos(n)n. converge or diverge? -
Chapter 2 Distributions The theory of distributions (sometimes called …
https://www.dpmms.cam.ac.uk/~cmw50/resources/M3P18/M3P18Ch2.pdf15 Oct 2021: Consider the sequence of distributions. uM =. Mm=M. D|m|δm. Let φ D () be any test function. ... u1φ = (u1? φ̃)(0) = (u2? φ̃)(0) = u2φ. for any test function φ, thus u1 = u2. -
neuro.dvi
https://www.dpmms.cam.ac.uk/~ik355/PAPERS/neuro.pdf5 Jun 2020: of the spike count in the data (as quantified by the Fano factor).This conclusion is rigorously justified with a t-test with a p-value of 5 104. ... Fanofactors and the percentage drop is zero, and the test statisticis t = r. -
ANALYSIS I EXAMPLES 1 G.P. Paternain Lent 2021 Comments ...
https://www.dpmms.cam.ac.uk/study/IA/AnalysisI/2020-2021/aI_1_21.pdf6 Feb 2021: Show also that. n=1(1)n1andiverges. [This shows that, in the alternating series test, it is essential that the moduliof the terms decrease as n increases.]. ... sequence. Prove that. j=1 ajbj converges. Deduce the alternating series test. Does the series. -
Mathematical Tripos: Part IB DJS/Lent 2015 Statistics: Example Sheet…
https://www.dpmms.cam.ac.uk/study/IB/Statistics/2014-2015/ex3.pdf23 Feb 2015: SXX/(n1)}1/2. Determine the distribution of T under H0, and hence. determine the size α likelihood ratio test. ... size α likelihood ratio test of equality of means rejects H0 if. -
PRINCIPLES OF STATISTICS – EXAMPLES 2/4 Part II, Michaelmas ...
https://www.dpmms.cam.ac.uk/study/II/PrinciplesOfStatistics/2023-2024/examples2-prob.pdf2 Oct 2023: From this limiting result: (i) derive a test for the hypothesis H0 : θ = θ0 vs. ... For all these models, derive explicit expressions for the likelihood ratio test statistic ofa simple hypothesis test of H0 : θ = θ0, θ0 Θ, vs.
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