Errata

8. Cowan, R. and Zabczyk, J. A new version of the best choice problem. Bull. Polish Acad. Sci. 24, 9  773-778 (1976).

In the first line of THEOREM 2, the ratio 36e/5 should have been typeset as 5/36e in agreement with the correct ratio in the second line. (Error detected by Daryl Daley.)

11. Cowan, R. An improved model for signalised intersections with vehicle-actuated control. J. Applied Probability 15 384-396 (1978).

p392. In mid-page, there is a formula for the conditional Laplace transform of Wi given J. The denominator of this formula should be (s + g)[1 - exp(-gb)], not simply (s + g). The missing factor correctly appears in the two formulae for conditional moments which follow immediately below. The error does, however, propagate in the formula for the Laplace transforms of T and of Gn given Rn (where [1 - exp(-gb)] should be crossed out).

p393. In eqn (3.2) the exponent of e is gb in both instances (not g / b as shown in one case ).

14. Cowan, R. Properties of ergodic random mosaic processes. Mathematische Nachrichten 97 89-102 (1980).

Trivia. V=83 in the first figure and M '(Br) in the inequality near the base of p94.

17. Cowan, R. Further results on single-lane traffic flow. J. Applied Probability 17 523-531 (1980).

Bottom of p524: "P{T* £  t}", that is, t not x.
Eqns (4.2) & (4.4): In curly brackets read {1 - exp(- g (b - a) [1 - h(a)])}

21. Cowan, R. An analysis of the fixed-cycle traffic light problem. J. Applied Probability 18 672-683 (1981).

The term (1 - z) in the denominator of formula (10) should read (1 - zs).

26. Cowan, R. A model for Random Packing of Disks in the Neighbourhood of One Disk. SIAM J. Applied Maths. 44, 4 839-853 (1984).

There has been a significant omission of text in the printed version. At the top of p842, it should read (in keeping with my original draft) ... "already-parked disk (say A) then it "rolls" around A to O by the shorter route and parks on O touching A. Formula (3) generalises (2) by assuming that each of these impeded approaches has an independent chance q of reaching O (where it will of course be touching A) and a complimentary chance 1 - q of locating itself elsewhere in the ensemble."

27. Cowan, R. A collection of problems in random geometry. Stochastic Geometry, Geometric Statistics, Stereology (eds. Weil and Ambartsumian) Teubner (1984).

In problem D, it should say "Imagine a congruent copy J of K being translated in the plane, ...". Delete the words "and rotated" which were unintended and make the problem silly.

36. Cowan, R. Hand evaluation in the game of Contract Bridge. J. Royal Statistical Society: Series C; Applied Statistics 36 58-71 (1987).

There is an inconsistency between Table 3 and certain references to Table 3 on p61, p70 and within the Table caption. In my original submission to the journal, Table 3 was consistent with the text. Inadvertently, when I reorganised the format of the Table so that it could fit comfortably on two pages of the journal, I used a computer file which listed the 4-3, 3-2 and 4-2 holdings without explicit counting of the equal numbers of 3-4, 2-3 and 2-4 holdings. For consistency with the text and the Table caption, numbers such as 140, 56, 56, 560, ... (for example in the 4-3 case) should be doubled. This oversight made during the re-formatting of Table 3 does not affect the paper in any other way; no mathematical errors have resulted from this oversight.

On the other hand, a handful of the TTP entries in Table 3 having been revised (some due to more sophisticated strategic analysis by me and a couple corrected by George Havas, Canberra mathematician and erstwhile bridge writer for "The Australian"). Changes to the paper's conclusions are numerically insignificant.

37. Cowan, R. A bivariate exponential distribution arising in random geometry. Annals Institute of Mathematical Statistics 39 103-111 (1987).

The expression in curly brackets should be the same in both parts of formula (1). In the second part, the expression for F(x, y), the symbol l is missing.

40. Cowan, R. and Morris, V. B. Division Rules for Polygonal Cells. J. Theoretical Biology 131 33-42 (1988).

Table 5: Column 1 should have header "k not equal to 3" (not "k=3"). In columns 4-7, it should be "k not equal to" (not "k=").

42. Cowan, R. Objects arranged randomly in space: an accessible theory. Adv. Appl. Prob. 21 543-569 (1989).

Section 6 on p551, is somewhat incomplete. It can happen that clumps are of infinite size, in which case the formulae in that section are not valid.

Formula (24) and its predecessor are correct, but the two formulae which follow it [for E(A) and E(L)] are not valid except in the convex case. Therefore, in the paragraph commencing "We now deal with random transects, ...", we must:

(a) change "Sh / 4pr2  (probes)" to  "S / 4pr2  (probes of convex D)";
(b) change "For a random probe of a connected D in R3," to "For a random probe of a convex D in R3,", whence the subscript h is dropped in the two following formulae;
(c) change "of same" to "of a connected D".

mid p559. In the formula for the conditional expectation of L given the event "script E", the "4" should be "2".

last formula on p565: change "r(ds)" to "n(ds)" (Greek nu)

53. Cowan, R. The Allocation of Offensive and Defensive Resources in a Territorial Game. J. Appl. Prob. 29, 190-195 (1992).

Tom Ferguson of UCLA pointed out a mistake in this paper. This led to a great deal more research eventually published with him (and Philip Yu) as #64. (See #64 for detail.)

65. Cowan, R. and Chen, S. The random division of faces in a planar graph. Adv. Appl. Prob. 28, 377-383 (1996).

Mid p381. Conditions should read "0 < x £ min(r,s)" not "0 £ x £ min(r,s)".

67. Cowan, R. Shapes of rectangular prisms after repeated random division. Adv. Appl. Prob. 29, 26-37 (1997)

Typing the equations on pp30-31 in LaTeX was a massive chore and I made a couple of slips. The third of the 6 integrals in (3) is missing a factor 1/x. The first term of the next equation, the massive equation spreading over pages 30-31, has been messed up. Function f in the integrand has only two arguments, so the big closing bracket comes after the second argument. Also the function g is missing. So the integrand should read as f(etc,etc) g(s) ds/s. Somewhat spoils my claim for the biggest solved equation ever published if I can't type it properly! Thanks to Francis Chen for picking it up.

 

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