**T**his post follows the original one on the headline of the USA Today I read during my flight to Toronto last month. I remind you that the unusual pattern was about observing four U.S. mass murders happening within four days, “for the first time in at least seven years”. Which means that the difference between the four dates is at most 3, not 4!

**I** asked my friend Anirban Das Gupta from Purdue University are the exact value of this probability and the first thing he pointed out was that I used a different meaning of “within 4″. He then went into an elaborate calculation to find an upper bound on this probability, upper bound that was way above my Monte Carlo approximation and my rough calculation of last post. I rechecked my R code and found it was not achieving the right approximation since one date was within 3 days of three other days, at least… I thus rewrote the following R code

T=10^6
four=rep(0,T)
for (t in 1:T){
day=sort(sample(1:365,30,rep=TRUE)) #30 random days
day=c(day,day[day>363]-365) #account for toric difference
tem=outer(day,day,"-")
four[t]=(max(apply(((tem>-1)&(tem<4)),1,sum)>3))
}
mean(four)

*[checked it was ok for two dates within 1 day, resulting in the birthday problem probability]* and found 0.070214, which is much larger than the earlier value and shows it takes an average 14 years for the “unlikely” event to happen! And the chances that it happens within seven years is 40%.

**A**nother coincidence relates to this evaluation, namely the fact that two elderly couples in France committed couple suicide within three days, last week. I however could not find the figures for the number of couple suicides per year. Maybe because it is extremely rare. Or undetected…

Filed under: Books, R, Statistics, Travel Tagged: birthday problem, coincidence, Conan Doyle, mass murders, Pittsburgh, Richard von Mises, The Sign of Four, Toronto, USA Today

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