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

19 Jun 2019: Xj = min(Tj , cj ), for 1 j n. extending the notation of (b) in the natural way.

30 Aug 2019: Ifj(θ) is such that tj < θ < tj1, what is the likelihood for θ?

30 Aug 2019: j>0. bj (U (n))tj =n1j=0. (1 t2j1). END OF PAPER. Part III, Paper 16.

30 Aug 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.

19 Jun 2019: Theeffects of recombination in the segment may be ignored. The time for which the samplehas j distinct ancestors is denoted by Tj , j = 2, 3,. ,

30 Aug 2019: Definition. The vector space IndGHV is defined to be the space with basis givenby the abstract symbols tj vi where t1,. , ... is given by g (tj vi) := ts hvi where ts is the unique coset representative suchthat gtj tsH, and h = t1s gtj.

30 Aug 2019: The effects of recombination in the segment may be ignored.The time for which the sample has j distinct ancestors is denoted by Tj , j = 2, 3,. ,

30 Aug 2019: connected to nodes ti and tj with arcs of infinite capacity, and each nodeti is connected to a node s′ with an arc of capacity w wi 1 and w = wn.

30 Aug 2019: an(gj)Tj. [Hint: The q-expansions of E4 and E6 are 1240. σ3(n)qn and 1504.