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30 Aug 2019: sequence = (tj ). nkj=1 such that tj < tjk.

30 Aug 2019: Part III, Paper 69. 3. 3. 1) Let Sk() be the space of splines of degree k1 spanned by the B-splines (Nj )nj=1on a knot sequence = (tj )nkj=1 ... such that tj < tjk.

30 Aug 2019: Show that the action of the left-invariant vector fields,. Tj (u) = iµji(u). ... ui,. on the matrix A is given by Tj A(u) = A(u) σj , and hence that Ti are generators of the.

30 Aug 2019: The variable tj (j = 1,. , 3) records the time interval under observationand takes the values 2, 4 or 6 months. ... logE(Yij|zi; xi; tj ). 1 E(Yij|zi; xi; tj )= α φZi βT xi δtj , (i = 1,. ,

17 Jun 2019: Assume p > q. Let Tj = inf{n > 1 : Xn = j} if this is finite, and Tj = otherwise.

19 Jun 2019: dependent toll Tj(yj ), and suppose each user selects a route in an attempt to mini-. ... Tj () so that the equilibrium flow pattern minimizes the average delay in the network.

30 Aug 2019: tj,. t6 with tj < tj1. The seventh individual is censoredat time c7 where t3 < c7 < t4.

30 Aug 2019: Justify your answers. Suppose now that, in addition to the delay Dj(yj), users of link j incur a traffic-dependent toll Tj(yj), and suppose each user selects a route ... Show that it is possible to choose the functions Tj() sothat the equilibrium flow

30 Aug 2019: Define f(tj) and h(tj) to be theprobability mass function and discrete hazard function of failing at tj respectively. ... Thelatter corresponds to the conditional probability of failing at tj, given still alive beyond theprevious failure time point tj1.

19 Jun 2019: where Si1, Si2 correspond respectively to the swimming times of the strong swimmer andthe not so strong swimmer in the ith pair, for 1 6 i 6 3, and Tj corresponds ... a) Show that for j = 4,. 8, Tj has probability density function.