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4 Mar 2009: Show that the likelihood ratio and Pearson’s chi-squared tests are identical to thosefor the independence test. ... Derive the likelihood ratio test of size α. 11. Statisticians A and B obtain independent samples X1,.

14 Oct 2009: 15. (Abel’s test) Let an and bn be real-valued functions on E R.

4 Mar 2009: Yn N(µY ,σ. 2), where σ is unknown. Derive the likelihood ratio test of size α of H0 : µX = µY againstH1 : µX 6= µY , showing in particular that it can ... are assigned only to one group or the other, we should considera two sample t-test.

14 Oct 2009: 15. (Abel’s test) Let an and bn be real-valued functions on E R.

9 Oct 2009: To test for linearity of α it is generally best to check α(λ.u+ µ.v) = λ.α(u) µ.α(v).

1 Oct 2009: http://www.skills.cam.ac.uk/. Do have a look. As it is still being developed, please test it for robustness, and supplyfeedback for the caretakers of the site.

12 Aug 2009: This also gives a test for minimality: if N iterations of theprocedure fail to decrease the level, then the model must be minimal.