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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

30 Aug 2019: A(t1)A(t2) A(t2n1)〉 = 0. 〈A(t1)A(t2) A(t2n)〉 =. all pairs. 〈A(ti)A(tj)〉〈A(tk)A(tl)〉. Considering carefully the number of pairs in the

30 Aug 2019: State the dual Cauchy identity. Let F (t) =. j>0 fj tj be a formal power series, where f0 = 1.

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

30 Aug 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,. ,

17 Jun 2019: Find the probability-generating functions of the random variables Hj and Tj.

30 Aug 2019: Let uji be the approximation at xi and tj ,i = 1,. ,

4 Aug 2022: Denote the kernel valuesfor indexed times as Rij k(ti, tj) and let R k(0,0).

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.

17 Jun 2019: for j 6= i. Prove that the random vectors Yj AjX are independent, and thatY (Y T1 ,. ,Y TJ )T has a multivariate normal distribution.[ Hint: Random vectors are independent if