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19 Jun 2019: 2. 1 Statistics in Medical Practice. Watson et al (British Medical Journal, 2005) describe a randomised trial of an interventionproviding child safety equipment to prevent injuries to under 5’s. ... Watson et al report an estimated rate ratio of 1.37

21 Aug 2019: 11F Probability. (a) Consider a Galton–Watson process (Xn). Prove that the extinction probability q isthe smallest non-negative solution of the equation q = F(q) where F(t) = ... In the case of a Galton–Watson process with. P(X1 = 1) = 1/4, P(X1 = 3)

30 Aug 2019: λeλ. 4. (i) Let T(n,p) be the Galton–Watson branching process with offspring distribution Bi(n, p).Show that, for p = (1 ε)/n, with ε > 0 small, the ... survival probability ρ = ρ(n,p) of thebinomial Galton–Watson branching process Tn,p

17 Jun 2019: Part IA, Paper 2 [TURN OVER. 8. 11F Probability. (a) Consider a Galton–Watson process (Xn). ... In the case of a Galton–Watson process with. P(X1 = 1) = 1/4, P(X1 = 3) = 3/4,.

30 Aug 2019: b) Explain briefly the class of (real) integrals appropriate for use of (i) Watson’slemma and (ii) Laplace’s method.

3 Jul 2024: Part II, Paper 3 [TURN OVER]. 18. 30C Asymptotic Methods. (a) State Watson’s lemma.

30 Aug 2019: b) State Watson’s lemma and sketch a proof of it. Suppose that.

30 Aug 2019: Watson’s lemma may be quoted without proof. 0. eu log u du = γ where γ is Euler′s constant.].

17 Jun 2019: State Watson’s lemma. Now consider the integral. J(λ) =. b. a.

5 Jan 2023: You may assume theform of the Nadaraya–Watson estimator.]. Part III, Paper 210.