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17 Jun 2019: 4]. 2A State the comparison test and the ratio test for assessing the convergence of theinfinite series.

30 Aug 2019: Part III, Paper 32. 3. 2 Statistics in Medical PracticeSupermarkets require processed meat suppliers to test a random sample of batches. ... 2 patients are recruited to each arm and a test statistic z2 is.

17 Jun 2019: The test for the disease has a probabilitya of producing a correct positive result when used on a sufferer and a probabilityb of producing a false positive result when used on ... The test ispositive when done on me. What is the probability that I am a

26 Nov 2019: Science of a DNA test - the science (and maths) behind having your genes sequenced.

17 Jun 2019: Use the generalized likelihood-ratio. test to derive the form of a test of the hypothesis H0 : µ = µ0 against H1 : µ 6= µ0. ... Explain carefully how the test should be implemented. 8C Optimization. State and prove the max-flow min-cut theorem for

19 Jun 2019: a) Conditional probabilities. A screening test has a probability 0.9 of being positivein true cases of a disease and a probability 0.995 of being negative in people without thedisease. ... The prevalence of the disease is 0.001. What is the probability

30 Aug 2019: iii) Show that the generalised likelihood ratio test of. H0 : V is a diagonal matrix. ... 14i=9. (yi. 16. 14k=9. yk. )2= 859.33. Describe how to test for lack of fit of this model.

17 Jun 2019: f (x | θ) = 12| x |θ1e|x|/Γ(θ), < x < ,. where Γ(θ) =0. yθ1eydy and θ > 1 is unknown. Find the most powerful test of size α,. ... Express thepower of the test as a function of α. Is your test uniformly most powerful for testing H0 : θ = 1

17 Jun 2019: a) Find the critical region of the likelihood ratio test of size α in terms of thesample mean X. ... c) Define what it means for a hypothesis test to be uniformly most powerful.

17 Jun 2019: Find auniformly most powerful size α test of H0 : θ 6 θ0 against H1 : θ > θ0, and find its powerfunction. ... Show that we may construct a different, randomised, size α test with the samepower function for θ > θ0.