Thomas S. Ferguson is a Professor in the Department of Mathematics and the Department of Statistics at the University of California at Los Angeles.

Mailing Address:

UCLA Department of Mathematics

520 Portola Plaza, Suite 6363

Los Angeles, CA 90095-1555

e-mail: tom@math.ucla.edu

- "Testing equality of players in a round-robin tournament", with F.
Thomas Bruss,
*The Mathematical Scientist*, Vol. 43 No. 2, Dec. (2018), 125-136. (pdf version.) - "Obliged Sums of Games" (2014). (pdf version 98K.)
- "House-Hunting Without Second Moments", with Michael J. Klass,
*Sequential Analysis*, 29, (2010), 236-244. (pdf version 148K.) - "The Sum-the-Odds Theorem with Application to a Stopping Game of
Sakaguchi",
*Mathematica Applicanda*44(1), (2016), 45-61. (pdf version 176K.) - "The Endgame in Poker", with Chris Ferguson, in
*Optimal Play - Mathematical Studies of Games and Gambling*, Stewart Ethier and William R. Eadington, eds. (2007) 79-106. Institute for the Study of Gambling and Commercial Gaming. (pdf version 236K.) - "U(0,1) Two-Person Poker Models", with Chris Ferguson and
Céphas Gawargy,
*Game Theory and Applications*, 12 (2007), 17-37, Nova Sci. Publ., N.Y. (pdf version 132K.) - "On the Borel and von Neumann Poker Models", with Chris Ferguson,
*Game Theory and Applications*, 9 (2003), 17-32, Nova Sci. Publ., N.Y. (pdf version 152K.) - "An Optimal Strategy for Sequential Classification on Partially Ordered Sets", with Curtis Tatsuoka, Statistics Probability and Letters, 68, (2004) 161-168. (pdf version 124K.)
- "Inverting Dirichlet Tessellations", with Rick Schoenberg and Cheng
Li,
*The Computer Journal*, 46 (2003), 76-83. (pdf version 400K.) - "Notes on a Stochastic Game with Information Structure", with Lloyd
Shapley and Robert Weber,
*International J. Game Theory*, 31 (2003), 223-228. (pdf version 204K.) - "Toetjes na", with Christian Genest,
*Mathematical Statistics and Applications: Festschrift for Constance van Eeden*, Marc Moore, Sorana Froda and Christian Léger, Editors, IMS Lecture Notes/Monograph Series, 42 (2003), 169-184. (Abstract, pdf version, 175K) - "Selection by Committee", in
*Advances in Dynamic Games*, A.S. Nowak and K. Szajowski eds., (2004) 183-188, Birkhäuser. By mistake, the published version is an earlier version without proofs. The correct version is here. (pdf version, 140K). - "Sequential Classification on Partially Ordered Sets", with Curtis Tatsuoka,
*J. R. Statist. Soc. B*, 65, (2003)143-157. (Abstract, pdf version 184K). - "On a Rao-Shanbhag Characterization of the Exponential/Geometric Distribution",
*Sankhya Series A*, 64, (2002) 246-255. (Abstract, pdf version 100K). - "High Risk and Competitive Investment Models", with F. Thomas Bruss,
*Ann. Applied Prob.*, 12 (2002), 1202-1226. (Abstract, pdf version 220K). - "Another Form of Matrix Nim",
*Electronic J. of Combinatorics*8 (No. 2) (2001), #R9. (Abstract, pdf version 88K). - "Kendall's tau for Serial Dependence", with Christian Genest and Marc
Hallin,
*Canadian J. Statist.*, 28 (2000) 587-604. (Abstract, pdf version 200K). - Some less recent papers.
- Unpublished papers.

- Math 167, Spring 2005, Game Theory .
- Statistics 200C, Spring 2010, Large Sample Theory.
- Statistics 596, Winter 2009, Game Theory for Statisticians.
- Additional Exercises and Errata for my
book,
*A Course in Large Sample Theory*, 1996, Chapman and Hall. - Solutions to Selected Exercises from my book, Mathematical Statistics - A Decision Theoretic Approach, in PostScript.

- Gateway to Mathematics Departments: Mathematics Department Servers

- The text, "Game Theory" has now been published by World Scientific under the title "A Course in Game Theory", (2020).
- Text: Linear Programming .
- Text: Optimal Stopping and Applications.
- Related Computer Programs.

- The joint distribution of two Bernoulli random variables, X and Y, is determined
by the 2 by 2 matrix of probabilities, p(i,j) = P(X=i,Y=j) for i=0,1 and j=0,1.
Suppose the (prior) distribution of (p(0,0),p(0,1),p(1,0),p(1,1)) is uniform
on the set {p(0,0)>0, p(0,1)>0, p(1,0)>0, p(1,1)>0,
p(0,0)+p(0,1)+p(1,0)+p(1,1)=1}. (This is the Dirichlet distribution with parameters
1,1,1,1.) Find the conditional distribution of the p(i,j) given that X and Y are
independent (i.e. given P(X=i,Y=j) = P(X=i)P(Y=j)).
Need a hint?
- A fair coin is tossed until it comes up heads and the number, X, of tails
before the first heads appears is recorded. Then two slips of paper are taken
and the number 3 to the power X is written on one of the slips and 3 to the
power X+1 is written on the other. One of these two slips is chosen at random
(probability 1/2 each) and given to you. It will have one of the numbers
1, 3 ,9, 27, 81, etc. written on it. After observing this number, call it z, you
are given the option of exchanging your slip for the other, unseen slip. Then
you are paid in dollars the number on the slip you possess. For which values
of z would you make the exchange? For which values of z would you make the
exchange if you had to pay a 10% commission to the broker who effects the exchange?
Need a hint?
- Kriegspiel is the game of chess in which the players are not allowed to
see the moves of the opponent. Instead, there is a "referee" who keeps track
of the each move on his own private board and tells the players if an attempted
move is legal. If an attempted move is legal, the player must play it; otherwise,
the player may try again. In addition, the referee announces all captures and
whether the captured object is a piece or a pawn. In the RAND rules, the referee
also announces checks, and possible captures by a pawn.
The question is: Can a blind person, hearing only the announcements of the referee, deduce a mate for one of the players? Need a hint?

- Two positive integers are chosen. The sum is revealed to logician A, and
the sum of the squares is revealed to logician B. Both A and B are given this
information and the information contained in this sentence. The conversation
between A and B goes as follows: B starts.
B: "I can't tell what the two numbers are."

A: "I can't tell what the two numbers are."

B: "I can't tell what the two numbers are."

A: "I can't tell what the two numbers are."

B: "I can't tell what the two numbers are."

A: "I can't tell what the two numbers are."

B: "Now I can tell what the two numbers are."What are the two numbers? Need a hint?

- The outcome of a certain experiment results in three (possibly dependent)
random variables, X, Y, Z, each taking values either zero or one. (So there
are 8 possible outcomes to the experiment.) Is it possible to set up such an
experiment so that
P(X = Y) + P(X = Z) + P(Y = Z) < 1 ?

Need a hint?