Publications by xi'an
Le Monde puzzle [#1155]
The weekly puzzle from Le Monde is another Sudoku challenge: Anahera and Wiremu play a game for T rounds. They successively pick a digit between 1 and 3, never repeating the previous one, and sum these digits. The last to play wins if the sum is a multiple of 3. Who is the winner for an optimal strategy? By a simple dynamic programming of the o...
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Le Monde puzzle [#1157]
The weekly puzzle from Le Monde is an empty (?) challenge: Kimmernaq and Aputsiaq play a game where Kimmernaq picks ten different integers between 1 and 100, and Aputsiaq must find a partition of these integers into two groups with identical sums. Who is winning? Indeed, if the sums are equal, then the sum of their sums is even, meaning the sum...
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Le Monde puzzle [#1159]
The weekly puzzle from Le Monde is quite similar to #1157: Is it possible to break the ten first integers, 1,…,10, into two groups such that the sum over the first group is equal to the product over the second? Is it possible that the second group is of cardinal 4? of cardinal 3? An exhaustive R search returns 3 solution by library(R.utils) b...
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understanding elections through statistics [book review]
A book to read most urgently if hoping to take an informed decision by 03 November! Written by a political scientist cum statistician, Ole Forsberg. (If you were thinking of another political scientist cum statistician, he wrote red state blue state a while ago! And is currently forecasting the outcome of the November election for The Economist.)...
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Fermat’s Riddle
·A Fermat-like riddle from the Riddler (with enough room to code on the margin) An arbitrary positive integer N is to be written as a difference of two distinct positive integers. What are the impossible cases and else can you provide a list of all distinct representations? Since the problem amounts to finding a>b>0 such that both (a+b) and...
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parking riddle
The Riddler of this week had a quick riddle: if one does want to avoid parallel parking a car over a six spot street, either the first spot is available or two consecutive spots are free. What is the probability this happens with 4 other cars already parked (at random)? While a derivation by combinatorics easily returns 9/15 as the probability to...
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artificial EM
When addressing an X validated question on the use of the EM algorithm when estimating a Normal mean, my first comment was that it was inappropriate since there is no missing data structure to anchor by (right preposition?). However I then reflected upon the infinite number of ways to demarginalise the normal density into a joint density ∫ f(x,...
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inverse Gaussian trick [or treat?]
When preparing my mid-term exam for my undergrad mathematical statistics course, I wanted to use the inverse Gaussian distribution IG(μ,λ) as an example of exponential family and include a random generator question. As shown above by a Fortran computer code from Michael, Schucany and Haas, a simple version can be based on simulating a χ²(1) v...
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sampling w/o replacement except when replacing
Another Riddle(r), considering a box with M myrtle balls and D dandelion balls. Drawing balls without replacement while they stay of the same color as the initial draw, else put back the last ball and repeat the process until all balls are drawn. The funny thing is that, unless M=0 or D=0, the probability to draw a myrtle ball at the end is alway...
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asymmetric information
The Riddler of 16 October had the following puzzle: Take a real number θ uniformly distributed over (0,100). Among three players, the winner is whoever guessed the closest price without going over θ. In the event all guesses exceeded θ, the contestant with the lowest (and therefore closest) guess is declared the winner. The second player knows...
1711 sym R (182 sym/1 pcs) 2 img