Chance News May June 2005
As the stakes increase, Prime-Number theory Moves Closer to Proof
Wall Street Journal, Science Journal, April 8. 2005, B1
Follow the points to find a Super Bowl champ
New York Times, 223 January, 2005, p 11
The explanation rests in a mathematical formula created by the baseball analyst Bill James and introduced in the 1980 Baseball Abstract. James determined that the record of a baseball team could be approximated by taking the square of team runs scored and dividing it by the square of team runs scored plus the square of team runs allowed. Because of its similarity to the geometric method for determining the sum of the angles in a right triangle, he called it the Pythagorean theorem.
How close is the Pythagorean theorem to the theorem that the sum of the angles in a triangle is 180 degrees?
P.S. Norton Star provided this picture observed by a student Tosin while walking in New York. Evidently New Yorkers are determined to not forget the quadradic formula!
This item was suggested by Peter Kostelec.
Case stirs fight on Jews, juries and execution
The New York Times, March 16, 2005
Dean E. Murphy
John R. Quatman was a prosecutor for 26 years in Alameda County California and is now a lawyer in Montana.
In 1987 Quatman was the prosecutor when Fred Freeman was found guilty of murder and robbery at a bar in Berkeley. The jury recommended the death penalty and Freeman was put on San Quentin's Death Row. He is now seeking to appeal his conviction.
Quatman has provided a habeas corpus petition (a petition typically used to appeal state criminal convictions to the federal courts when the petitioner believes his constitutional rights were violated by state procedure) stating that at the 1987 trial the late Judge Stanley Golde, during the jury selection, advised Quatman that no Jew would vote to send a defendant to the gas chamber. In his petition, Quatman said that Golde helped him keep Jews off the jury. And Quatman recommended the death penalty for Freeman.
Quatman claimed that it was standard practice to exclude Jewish jurors in death sentences and this practice extended to African-American women, though this was not a problem for the Freeman trial. In rulings going back to 1880 the United States Supreme Court has ruled that it is illegal to reject jurors on the basis of race, and the California Supreme court in 1978 extended that prohibition to religion.
On Tuesday the California Supreme Court will investigate Quatman's sworn declaration. If they find Quatman's claims are credible Freeman will likely get a new trial.
Quatman's declaration is being used in the appeal of another Alameda inmate, Mark Schmeck. The Habeas Corpus Resource Center (HCRC) provides counsel to represent indigent (poor) men and women under sentence of death in California.The HCRC is representing Freeman in his appeal. Working with Schmeck's lawyers, the HCRC reviewed the jury selection in 25 capital trials in Alameda from 1984 to 1994.
The review found that 12 people who identified themselves as Jews were called to the jury box and the prosecution rejected all 12. They also found that of the 17 who had surnames judged to be Jewish names, the prosecution rejected 15. Overall they found that non-Jews were excluded at a rate of 49.97% and Jews and those with Jewish surnames were excluded at a rate of 93.10%.
Cliff Gardner, a lawyer for Mr. Schmeck, said that the statistics from the 10-year review of the capital trials spoke for themselves. Mathematician Phillip Farmer said that the probability of randomly striking 27 of 29 Jews is less than 1 in 1.6 million.
(1) How do you think Farmer got his 1 in 1.6 million probability?
(2) What problems are there in trying to estimate the probability that an event in the past occurred?
(3) After this was written, it was reported in the New York Times (April 6, 2005) that Judge Kevin Murphy, of Santa Clara County Superior Court, concluded that Quatman lied when he said an Alameda County judge encouraged him to exclude Jews from a jury in the trial of a man sentenced to death in 1987. The article says that Judge Murphy's opinion will be forwarded to the Supreme Court for a final ruling.
Evidently, Murphy's conclusion was reached on the basis of interviews with Quatman and others involved in the case. The statistical evidence seems not to have played a role in his decision. Do you think it should have?