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8 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?

8 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.

18 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?

24 Jan 2010: 1. Ask your supervisor to test you on the sheet of common distributions handed out inlectures.

24 Feb 2010: 9. Derive from first principles the form of the size α likelihood ratio test of equality ofmeans in the one-way ANOVA model of 4.

23 Feb 2010: In each case, explain how would you test these hypotheses, assuming that thefitted values in each cell are not too small.

29 Jan 2010: How would you perform the hypothesis test?[Hint: from the first example sheet rank(P ) = p, and rank(I P ) = n p.Similar arguments give that rank(P0) = p0.

12 Oct 2010: 2. In practice we may simplify the test for equivalence given by Theorem 12 by spe-cialisation, as in Lemma 10: it is easier to check that a binary quartic has ... 9. work with bi-quartics. To test for a bi-linear factor of F (X1, Y1, X2, Y2), it is

15 Oct 2010: To test for linearity of α it is generally best to check α(λ.u µ.v) = λ.α(u) µ.α(v).

15 Oct 2010: 15. (Abel’s test) Let an and bn be real-valued functions on E R.

12 Oct 2010: Therefore our local solubility tests. HEIGHT BOUNDS FOR COVERINGS OF ELLIPTIC CURVES 5. ... Assume char(k) 6= 2, 3. Then one way to test whether a binary.

19 Oct 2010: Height Bounds for n-Coverings. Graham Sills. Trinity College, Cambridge. June 11, 2010. A thesis submitted for the. degree of Doctor of Philosophy. at the University of Cambridge. Email: gs300@cam.ac.uk. 1. Summary. This thesis aims to develop the