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16 Feb 2012: 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.

20 Jan 2012: 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?

24 Jan 2012: 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). nconverge or diverge?

9 Mar 2012: b) The statistic -3.1 can be used to test for a linear trend in year. ... Explain. (e) The null deviance was 140.42. Construct an appropriate statistic for test-ing a time trend.

28 Feb 2012: determine the size α likelihood ratio test. 3. Suppose that X1,. , ... nI , show from first principles that the. size α likelihood ratio test of equality of means rejects H0 if.

27 Jan 2012: Comments and corrections to s.pitts@statslab.cam.ac.uk. 1. Ask your supervisor to test you on the sheet of common distributions handed out inlectures.

10 Feb 2012: H0. How would you perform the hypothesis test?[Hint: from the first example sheet rank(P) = p, and rank(IP) = np.Similar arguments give that rank(P0) = p0.

19 Jul 2012: 1051–14. 1.5.2. Christodoulou memory. — Gravitational wave experiments can be idealized asthe study of the relative displacement of two test masses m1, m2 with respect to a thirdreference mass ... r2χ̂. Thus, for a suitable configuration of the

27 Nov 2012: Part III Differential GeometryLecture Notes. Mihalis Dafermos. Contents. 1 Introduction 3. 1.1 From smooth surfaces to smooth manifolds. 31.2 What defines geometry? 51.3 Geometry, curvature, topology. 7. 1.3.1 Aside: Hyperbolic space and