Lecture 14

Short· History. Galileo (1564-1642), an Italian m athematic~, was the
first to attempt at a quantitative measure o.fpro.bability while dealing with some
problems related to the theory o.f dice in gambiing. Bul the flfSt fo.undatio.n o.f the
mathematical theory ifprobabilily was laid in the mid-seventeenth century by lwo.
French mathematicians, B. Pascal (1623-1662) andP. Fermat (1601-1665), while.
solving a number of problems posed by French gambler and noble man Chevalier-
De-Mere to Pascal. The famous problem of points posed by De-Mere to Pascal
is : "Two persons playa game of chance. The person who ftrst gains a certain
number of pOints wins the stake. They stop playing before the game is completed.
How is,th~ stake to be decided on the.basis of the number of points each has won?"
The two mathematicians after a lengthy correspondence between themselves
ultimately solved this problem and dfis correspondence laid the fust foundation of
the science of probability. Next stalwart in this fteld was J. . Bernoulli (1654-1705)
whose Treatise on Probability was publiShed posthwnously by his nephew N.
Bernoulli in 1719. De"Moivre (1667-1754) also did considerable work in this field
and published his famous Doctrine of Chances in 1718. Other.:main contributors
ai e: T. Bayes (Inverse probability),P.S. Laplace (1749-1827) who after extensive
research over a number of ·years ftnally published Theoric analytique des prob-
abilities in 1812. In addition 10 these, other outstanding cOntributors are Levy,
Mises and R.A. Fisher.
Russian mathematicians also have made very valuable contribUtions to the
modem theory of probability. Chief contributors, to mention only a few of them
are,: Chebyshev (1821-94) who foUnded the Russian School of Statisticians;
A. Markoff (1856-1922); Liapounoff (Central Limit Theorem); A. Khintchine
(law of Large Numbers) and A. Kolmogorov, who axibmi.sed the calculus of
probability. .