Search

30 Aug 2019: a) Use suffix notation to prove that. a (b c) = c (a b). ... r (a b b c c a) = a (b c),.

30 Aug 2019: 2. (i) State and prove the Erdős–Ko–Rado Theorem. (ii) Two set systems, A and B, are called cross-intersecting if A B 6= whenever A Aand B B. ... f(r, s) elements such thatA B X 6= for all A A and B B.

19 Jun 2019: µ(B) =. B. dp dθ. for B (0,) [0, 2π). A random countable set Φ R2 is defined to consist of allintersections of pairs of lines in Π.

19 Jun 2019: For the particular choice. ψ(x) = min{b, max{x,b}}, b < :. (i) Find the asymptotic variance V (ψ, Φ), where Φ is the standard normal distri-bution;. ... ii) Verify that the estimator is B-robust, by determining an explicit bound on theinfluence

19 Jun 2019: b) Let X be a random variable such that EX2 < and E(X | G. ... n0. b) Let(Xn. )n0 be a positive supermartingale. For fixed a, b, b > a > 0, we put N0 = 1.

19 Jun 2019: 40%. (b) Describe and compare hierarchical and partitioning methods for clustering of sam-ples. ... theoutput distribution is specified by B = b(j,k).

19 Jun 2019: b) there exists a positive random variable ν, P (ν > 0) = 1, with E ‖νA1‖ < suchthat A0 = E (νA1). ... 2θ, or otherwise, derive an. expression for E(eθTa,b. )for each b, < b <. Hence, or otherwise, show that, for t > 0,. P (Ta,b 6 t) = e2abΦ(.

19 Jun 2019: 6]. 3 Let Ta,b denote the first hitting time of the line a bs by a standard Brownianmotion, where a > 0 and < b < and let Ta = Ta,0 represent the ... 2θ or otherwise, derive an expression. for E(eθTa,b. )for each b, < b <. [8]. Hence, or otherwise,

30 Aug 2019: where A = A(t z) and B = B(t z) are non-zero smooth functions of t z. ... d) Show that the vacuum Einstein equation Rab = 0 reduces to A′′/A B′′/B = 0.

17 Jun 2019: Show that:. (a) A a = B b = C c = 1,. ... b) A b = A c = 0,. (c) A, B and C are non-coplanar.