User:Koulourlatos/sandbox

Florence Nightingale David


 * Biography and Education
 * 1) Born in London on August 23, 1909.
 * 2) Schooling was interrupted by World War 1.
 * 3) Attended Bedford College for Women and received a degree in Mathematics in 1931.
 * 4) Attended University College in London for her doctorate in 1938.


 * Career
 * 1) Returned to University College in London after World War 2 and became a Professor in 1962.
 * 2) Moved to California and became a Professor and the Chair of the Department of Statistics at University of California, Riverside in 1968.
 * 3) Retired in 1977 but moved to the University of California, Berkley where she continued to teach and do research in Biostatistics.


 * Contributions
 * Combinatorics


 * Clear exposition of complicated methods of combinatorics.


 * Correlation Coefficient


 * Computed solutions of complicated difficult multiple integrals, using the distribution of the correlation coefficient.
 * Using Correlation Coefficient, F. N. David saw the following:


 * Calculated the distribution on a hand cranked mechanical calculator known as a Brunsviga.
 * Used Correlation Coefficient:
 * ρ= (cov(X,Y))/(σ_1 σ_2 ).
 * The parameter ρ measures how the two random variables X and Y vary together.
 * To see the linear relationship between X and Y and what happens when ρ = 0 or when ρ = +1 or -1.
 * When ρ = 0 the two random variables are uncorrelated. They are independent.  When +1 or -1, the there is a perfect linear :::relationship between X and Y.


 * Origins and History of Probability and Statistical Ideas


 * Wrote a book on history of probability, using problems thought of by famous mathematicians and scientists like Cardano and Galileo. It was called "Games, Gods and Gambling: The Origins and History of Probability" and states the following:


 * Idea of combinations was noted briefly by the Greeks attempting calculations, and the Arabs and the Chinese also indulged in them
 * First dice game mentioned in literature of the Christian era was called Hazard.
 * Played with 2 or 3 dice
 * Thought to have been brought to Europe by the knights returning from the Crusades.
 * Dante (1265-1321) mentions this game.
 * A commentor of Dante puts further thought into this game:
 * The thought was that with 3 dice, the lowest number you can get is 2, an ace for every die. Achieving a 4 can be done with 3 die by having a two one one die and aces on the other two dice.


 * Cardano
 * 3 dice are thrown: there are the same number of ways to throw a 9 as there are a 10.
 * For a 9:(621) (531) (522) (441) (432) (333) and for 10: (631) (622) (541) (532) (442) (433)
 * From this, Cardano found that the probability of throwing a 9 is less than that of throwing a 10


 * Galileo
 * Wrote about die-throwing sometime between 1613 and 1623
 * Essentially thought about Cardano's problem, about the probability of throwing a 9 is less than throwing a 10. Galileo had the following to say:
 * Certain numbers have the ability to be thrown because there are more ways to create that number. Although 9 and 10 have the same number of ways to be created, 10 is considered by dice players to be more common than 9.