Fred M. Hoppe

Position: Professor of Mathematics and Statistics
  • B.Sc.   University of Toronto   (Physics)
  • M.Sc.   Weizmann Institute of Science   (Mathematics)
  • M.A.   Princeton University   (Applied and Computational Mathematics and Statistics)
  • Ph.D.   Princeton University   (Applied and Computational Mathematics and Statistics)
  • Fellow, Institute of Mathematical Statistics
  • Foundation Fellow, Institute of Combinatorics and its Applications

Address: Hamilton Hall 205
Department of Mathematics and Statistics
McMaster University, 1280 Main St. West
Hamilton, ON L9H 6R8
Phone: (905) 525-9140 Ext. 24688
Fax: (905) 522-0935

Research Interests

My work lies in applications of probability, statistics, and stochastic processes. My papers have been in the following areas:

I am also an Associate Member of the Department of Engineering Physics.

My Erdos Number is 3 based on the sequence

Selected Recent Publications

Recent Refereed Conference Proceedings

Current/Recent Graduate Students

Dan Pun-quach (Ph.D.) - graduated September 2015. "A Statistical Framework for Distinguishing between Aleatory and Epistemic Uncertainties in the Best-Estimate Plus Uncertainty (BEPU) Nuclear Safety Analyses"
Xingli Wei (Ph.D.) - graduated June 2014. "Parameter Estimation and Prediction Interval Construction for Location-Scale Models with Nuclear Applications"
Jungtae Kim (M.Sc.) - graduated January 2012. "Optimal Strategy Hand-Rank Table for Jacks or Better, Double Bonus, and Joker Wild Video Poker"


I am very interested in applications of probability and statistics to industry and business. The main companies for whom I have consulted are in the nuclear sector and include AMEC-NSS, Nuclear Safety Solutions, Ontario Power Generation, Ontario Hydro, and the CANDU Owners Group, but I have also done work for the Ontario Lottery and Gaming Corporation, the Western Canada Lottery Corporation, Fallsview Casino, the Canadian Nuclear Safety Commission, Monserco, Ontario Workplace Safety Insurance Board, Kraft Foods, Nestles, and the Ontario College of Respitatory Therapists, as well as various law firms.
I welcome queries from the public.


Since the Maclean's Magazine article appeared, quoting my calculations for Lotto, and comparing the chance of winning to the chance of tossing 24 heads in a row (This description covered Lotto 6/49 at the time. It needs to be updated for the new prize structure.) I have often been contacted by the media when there is lottery fever or some lottery question. This happened most recently in October 2006 the day of a CBC Fifth Estate program concerning allegations of fraud by lottery retailers. I was quoted by the Toronto Star as saying that no more than about 20 retailers should have won major prizes. (This story even appeared in the Canadian Chinese press.)

I computed this number based on the information given to me by both the Star and CHTV. My understanding was that the figures supplied applied only to Lotto Super 7 and my estimate therefore only applied to this particular lottery. Unfortunately, this information was omitted from the article, but happily, the article did say that my conclusion "depend[ed] on assumptions made about how many retailers play the lottery."

A Few Lottery Clips in the Media


Chance is an outstanding source of probability and statistics ideas as applied to everyday life to which I've occasionally contributed items with pedagogic value. Here are four that would be of interest to high school and university students.


I am a strong proponent of the use of Excel in teaching undergraduate statistics. Even in my consulting, I have found Excel to be a handy tool for scientists and engineers for examining data, plotting, and suggesting models. Of course, Excel does have some known problems, for instance in simulation. I have written a number of macros for use in my Statistics 1cc3 classes at McMaster University. This archive of macros accompanies the 4th edition of my Excel Manual for The Basic Practice of Statistics, W. H. Freeman, NY, 2006 used in conjunction with David Moore's popular The Basic Practice of Statistics, W. H. Freeman, NY, 2006. The regression to the mean macro S1cc3_corr.xls simulates 1000 pairs of observations (x, y) from a population with a correlation given by a parameter "rho" (Greek letter). It draws the line of equal percentiles and also the regression line. The user can change the value of rho with the slider. Each time the sample is taken, the value of the correlation r computed from the sample is shown. Observe that r is close to rho but does vary from sample to sample. Repeated use of macro shows how scatterplots with different correlations might appear. The sampling simulation macro samsim.xls showing histograms of 1000 SRSs of size 100 from a population. User can change the population proportion. The macro gbmsim.xls simulates stock market prices using geometric Brownian motion.
If you have any questions or suggestions for other macros please contact me. (If you encounter a run-time error in the boxplot macro using the RUN button, then access the macro from the menu Tools --> Macros --> bp--- open_dialog_box.)

September 2015