Chance News 56
I can calculate the motion of heavenly
bodies but not the madness of people
After losing a fortune in the
South Sea Company bubble of 1720
Trying is the first step towards failure. -- Homer Simpson
This forsooth is from the October 2009 RSS Forsooth.
Of course in those days we worked on the assumption that
everything was normally distributed and we have seen in the
last few months that there is no such thing as a normal distribution.
Scientific Computing World
You can see the context of this comment here.
Minimizing the number of coins jingling in your pocket
Do We Need a 37-Cent Coin? Steven d. Levitt, October 6, 2009, Freakonomics Blog, The New York Times.
The current system of coins in the United States is inefficient. Patrick DeJarnette studied this problem and his work was highlighted in the Freakonomics blog. Dr. DeJarnette makes two assumptions.
1. Some combination of coins must reach every integer value in [0,99].
2. Probability of a transaction resulting in value v is uniform from [0,99].
Under this system, the average number of coins that you would receive in change during a random transaction would be 4.7. The system that would work better is rather bizzarre.
The most efficient systems? The penny, 3-cent piece, 11-cent piece, 37-cent piece, and (1,3,11,38) are tied at 4.10 coins per transaction.
Such a set of coins would be evocative of the monetary system in the Harry Potter books.
The article goes on to discuss systems where the coins are more conveniently priced and which single change in coins would lead to the greatest savings.
Submitted by Steve Simon
1. Minimizing the number of coins received in change is not the only criteria for a set of coin denominations. What other criteria make sense.
2. Is it logical to assume a uniform distribution in this problem?
3. What coin could be added to the current mix of coins to minimize the number of coins given in change.
Carrying a gun increases risk of getting shot and killed
October 06 2009
Here we read:
It would be impractical – not to say unethical – to randomly assign volunteers to carry a gun or not and see what happens. So Charles Branas's team at the University of Pennsylvania analysed 677 shootings over two-and-a-half years to discover whether victims were carrying at the time, and compared them to other Philly residents of similar age, sex and ethnicity. The team also accounted for other potentially confounding differences, such as the socioeconomic status of their neighbourhood.
Objectives. We investigated the possible relationship between being shot in an assault and possession of a gun at the time.
Methods. We enrolled 677 case participants that had been shot in an assault and 684 population-based control participants within Philadelphia, PA, from 2003 to 2006. We adjusted odds ratios for confounding variables.
Results. After adjustment, individuals in possession of a gun were 4.46 (P<.05) times more likely to be shot in an assault than those not in possession. Among gun assaults where the victim had at least some chance to resist, this adjusted odds ratio increased to 5.45 (P<.05).
Conclusions. On average, guns did not protect those who possessed them from being shot in an assault. Although successful defensive gun uses occur each year, the probability of success may be low for civilian gun users in urban areas. Such users should reconsider their possession of guns or, at least, understand that regular possession necessitates careful safety countermeasures.