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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,.

26 Nov 2019: Thanks to Fran Watson who has generously donated this five star bird house to the cmsgreenimpact team for use on site.

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

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: Watson estimator m̂Kn,h. Now suppose that m is differentiable, with m′ L, and V is bounded by σ2 > 0.Prove that if n > 2h1, and x [0,1],.

17 Jun 2019: Paper 4. 13. 21C Mathematical Methods. State Watson’s lemma giving an asymptotic expansion as λ for an integral ofthe form.

30 Aug 2019: the Nadaraya–Watson (local constant)estimator m̂(x).

17 Jun 2019: State Watson’s lemma describing the asymptotic behaviour ofI(λ) as λ, and determine an expression for the general term in the asymptotic series.

30 Aug 2019: 4. 5. Define the fixed and random design regression models. Carefully define theNadaraya-Watson estimator and the local polynomial regression estimator.