## Approximate Computation of Expectations |

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abstract analogous antisymmetric apply approach argument basic assumption basic idea binary expansion binomial distribution bound the remainder bounded function bounded piecewise continuous bounded solution choose completes the proof compute conditional distribution conditional expectation continuous and piecewise Corollary cycles of length defined derive diagram I.28 differential equation distributed random variables Eh(W exchangeable pair X,X Finally finite follows function f given identically distributed random inclusion mapping independent identically distributed independent random variables inequality Lecture VII Lemma I.2 let us look linear mapping linear space method normal approximation problem NORMAL APPROXIMATION THEOREM number of isolated obtain ordered pair piecewise continuously differentiable Poisson approximation Poisson distribution possible probability density function probability space proof of Lemma prove random allocations random graphs random permutation real random variables right hand side satisfies standard normal sum of independent sup|h sup|h-Nh tion uniformly distributed verify wf(w yp(y)dy

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Page 164 - On the rate of convergence in the central limit theorem for weakly dependent random variables.

Page 6 - We are grateful to the National Science Foundation for its support of this work through grant CHE-7606099.

Page 37 - Xj,J = l,2,... be independent identically distributed random variables with mean 0 and variance 1 and let T^ =п1/2(Х...

Page 34 - Eqns. (1) and (2), we define the recombination current fluctuation to be the sum of the last two terms on the right hand side, i, (t) = - e dn(tVdt = en(t) / T - efn(t).

Page 5 - One reason for this is that such random variables may be used to approximate the distribution of the number of successes in a large number of...

Page 51 - These include the number of ones in the binary expansion of a random integer, Latin rectangles, random allocations, and the number of isolated trees in a random graph.

Page 164 - YAMAMOTO, K. (1951). On the asymptotic number of Latin rectangles. Japan J. Math. 21, 113-119.

Page 133 - N*, is a random variable whose distribution is the same as the conditional distribution of...

Page 29 - I shall give a proof of this lemma although it is the well-known fact that the zeroth reduced homology group of a connected augmented simplical complex is 0.

Page 128 - Two such sequences determine the same cycle if and only if one is a cyclic permutation of the other.