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NATURAL SCIENCES TRIPOS Part IA Monday 7 June 2004 ...
https://www.maths.cam.ac.uk/undergradnst/files/2004/PaperNST_IA_1.pdf17 Jun 2019: 4]. 2A State the comparison test and the ratio test for assessing the convergence of theinfinite series. -
MATHEMATICAL TRIPOS Part III Friday, 7 June, 2013 1:30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2013/paper_32.pdf30 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. -
If you have anything you would like to be ...
https://www.maths.cam.ac.uk/internal/files/faculty-bulletins/Issue_49-04June2018.pdf26 Nov 2019: Science of a DNA test - the science (and maths) behind having your genes sequenced. -
NATURAL SCIENCES TRIPOS Part IA Wednesday 11 June 2003 ...
https://www.maths.cam.ac.uk/undergradnst/files/2003/PaperNST_IA_2.pdf17 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 -
MATHEMATICAL TRIPOS Part IB Tuesday 5 June 2007 9 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2007/PaperIB_1.pdf17 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 -
M. PHIL. IN COMPUTATIONAL BIOLOGY Friday 16 May 2008 ...
https://www.maths.cam.ac.uk/postgrad/mphil/files/misc/2008Paper_CompBiology.pdf19 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 -
MATHEMATICAL TRIPOS Part III Friday 6 June, 2003 1:30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2003/Paper42.pdf30 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. -
MATHEMATICAL TRIPOS Part IB Wednesday 6 June 2007 1.30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2007/PaperIB_2.pdf17 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 -
MATHEMATICAL TRIPOS Part IB Tuesday, 4 June, 2019 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2019/paperib_1_2019.pdf17 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. -
MATHEMATICAL TRIPOS Part II Alternative B Tuesday 4 June ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2002/PaperIIB_2.pdf17 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.
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