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18 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.

6 Mar 2013: 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.

26 Feb 2013: 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.

23 Jan 2013: Doesn. 1n log n log log n. converge? 10. Prove the root test, which says the following. ... the series diverges. What happens if a = 1? Add this test to your series grid.

10 Oct 2013: To test for linearity of α it is generally best to check α(λ.u µ.v) = λ.α(u) µ.α(v).

24 Jan 2013: 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.

19 Jan 2013: Hint: Use the Weierstrass M-test fromAnalysis II to show that f is locally uniformly convergent.].

15 Feb 2013: How would you perform the hypothesis test?[Hint: from the first example sheet rank(P) = p, and rank(I P) = np.Similar arguments give that rank(P0) = p0.

15 Aug 2013: It should be a single sentence. • A theorem.• A hypothesis you wish to test.• Example: Simple representations of semi.

7 Aug 2013: Butthere are two things we can test - their consistency, and their extensionalequality. ... They focus on input-output behaviour. In the Turing Test, If the re-sponse of a machine is indistinguishable from that of a person then we regardthem as equivalent