Chance News 50: Difference between revisions

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Submitted by Margaret Cibes<br>
Submitted by Margaret Cibes<br>


==Item5==
==A Probability puzzle==


The [http://www.msri.org/ Mathematical Science Research Institute/] has a monthly newsletter called the The Emissary.This has among other things a puzzle.  For the
The [http://www.msri.org/ Mathematical Science Research Institute/] has a monthly newsletter called the The Emissary.This has among other things a puzzle.  For the
Comment: This puzzle is due to Thomas Colhurst.
5. Find three random variables X, Y, Z, each uniformly distributed
on [0; 1], such that their sum is constant. (Since each random variable
has expectation 1
2 , the sum must in fact be 3

Revision as of 20:26, 20 June 2009

Quotation

Forsooths

Swine flu pandemonium III

"Fourth Connecticut Resident With Swine Flu Dies" by Arielle Levin Becker, The Hartford Courant, June 19, 2009
See Chance News 49 [1] for two earlier stories about the second and third cases of swine flu in Connecticut.

A fourth Connecticut death has been "linked" to swine flu.

The person was between 40 and 49 years old and had underlying medical conditions that increased the risk for serious illness from flu, the state Department of Public health said.

To date there have been 767 confirmed cases of swine flu, 28 of the cases had been hospitalized, and 19 of the hospitalized were from the largest cities. All four deaths occurred in people with other medical problems who were hospitalized at the time of death.

Here is the data to date about Connecticut deaths from swine flu:
1 death – 395 confirmed cases – June 4
2 deaths – 637 confirmed cases – June 11
3 deaths – 693 confirmed cases – June 15
4 deaths – 767 confirmed cases – June 17

Discussion

1. Would you advise Connecticut residents to move out of large cities to avoid swine flu? Could the victims have been identified as being from the largest cities because they died in large city hospitals, as opposed to having resided in large cities?
2. Would you advise Connecticut residents with swine flu to avoid hospitals?

Submitted by Margaret Cibes

Role of luck in golf

"Winning a Major May Just Be a Matter of Luck", by Jason Turbow, The Wall Street Journal, June 19, 2009

Using data from every PGA leadership board from 1998 to 2001, two business professors, from University of North Carolina and Dartmouth, have used "cubic spline functions" to try to explain the role of luck in professional golf.

"If being on the leaderboard at the end of a tournament was due entirely to skill, we would see the same names every week," said [the Dartmouth researcher]."

Their model aims to predict an individual's score in a tournament based on an estimate of the person's "intrinsic skill level independent of variables like course difficulty and variations over time." A golfer with a higher tournament score than predicted was considered to have had good luck; one with a lower score was considered to have had bad luck.

[I]n all the events the researchers studied, Mr. Woods was the only golfer to win a tournament despite suffering from negative luck.

The brief article includes a table [2] of expected score, actual score, and "luck factor" for players Tiger Woods, Ernie Els, Vijay Singh, Phil Mickelson, Sergio Garcia, and Jim Furyk, in the 2000 U.S. Open.

Submitted by Margaret Cibes

Baseball: More education, more victories?

"Who Has the Brainiest Team in Baseball?", by Jason Turbow, The Wall Street Journal, June 16, 2009

The author studied "30 team media guides" to try to determine whether there is "a correlation between education and victories" in professional baseball. He compared team standings with players' and managers' undergraduate degrees. He found that only about two dozen major league players or managers had undergraduate degrees.

[T]hree "All-Brains" division leaders -- Oakland, Arizona and Washington -- are in last place in real life, while Texas and the Dodgers were last in their divisions in smarts but first in the standings.

Two bloggers [3] wrote:

(1) "[A]re these results really surprising? The best teams are the best teams because they have more good players than the other teams. Good players are likely to have been A) so talented at baseball as to have little incentive to work hard at school and B) so dedicated to the sport that academics would have suffered. If you're a marginal major league talent like Breslow, it makes sense to get a degree with better earnings potential. Not so for the Alex Rodriguezes [sic] and Barry Bondses [sic] of the world."

(2) "How about instead of looking at university experience, check out something that almost every player (from the U.S., at least) would have: SAT scores. Surely there is the occasional ballplayer with a stratospheric score who still opts for baseball over college."

Submitted by Margaret Cibes

Keeping up with the Joneses by lowering utility bills

“Greening With Envy”, by Bonnie Tsui, The Atlantic, August 2009
Robert Cialdini, a social psychologist at Arizona State University, tested 4 different hotel reuse-towels signs to test how well guests responded:

The first sign had the traditional message, asking guests to “do it for the environment.” The second asked guests to “cooperate with the hotel” and “be our partner in this cause” (12 percent less effective than the first). The third stated that the majority of guests in the hotel reused towels at least once during their stay (18 percent more effective). The last message was even more specific: it said that the majority of guests “in this room” had reused their towels. It produced a 33 percent increase in response behavior over the traditional message.

As the chief scientist for Positive Energy, Cialdini is now applying what he learned to encouraging utility consumers to conserve energy by letting them know how much energy they use relative to their neighbors. Based on his software’s analysis of a neighborhood’s energy usage, a utility company can send monthly bills to consumers with information about how a particular consumer’s usage compared to that of his/her neighbors. For example, a consumer who used “58 percent less electricity” might receive a row of smiley faces, while one who used “39 percent more” might receive no smiley faces, a notice that it cost him/her $741 extra, and tips for improvement.
In Sacramento,

people who received personalized “compared with your neighbors” data on their statements reduced their energy use by more than 2 percent over the course of a year. … [W]ith the pilot sample of 35,000 homes, it’s the equivalent of taking 700 homes off the grid. And the cost to the utility is minor: for every dollar a utility spends on a solar power plant, it produces 3 to 4 kilowatt-hours; for every dollar a utility spends on the energy reports, it saves 10 times that.

Submitted by Margaret Cibes

A Probability puzzle

The Mathematical Science Research Institute/ has a monthly newsletter called the The Emissary.This has among other things a puzzle. For the Comment: This puzzle is due to Thomas Colhurst. 5. Find three random variables X, Y, Z, each uniformly distributed on [0; 1], such that their sum is constant. (Since each random variable has expectation 1 2 , the sum must in fact be 3