2. Gerolamo Cardano September 24September 24, 1501 — September 21, 15761501September 211576 was an Italian Renaissance mathematician, physician, astrologer and gamblerItalianRenaissancemathematicianphysicianastrologergambler Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and chess player. His book about games of chance,chess Liber de ludo aleae, written in the 1560s, but not published until 1663, contains the first systematic treatment of probability, as well as a section onprobability effective cheating methods.

3. Through his correspondence with Blaise PascalBlaise Pascal in 1654, Fermat and Pascal helped lay the fundamental groundwork for the theory of probability. From this brief butprobability productive collaboration on the problem of points, they areproblem of points now regarded as joint founders of probability theory. Pierre de Fermat 17 August17 August 1601 – 12 January 1665160112 January1665 France Blaise PascaJune 19, 1623 – August 19, 1662

4. Jacob Bernoulli 27 December 1654 – 16 August 1705 Jacob is best known for the work Ars ConjectandiArs Conjectandi (The Art of Conjecture), published eight years after his death in 1713 In this work, he described the known results in probability theory and in enumeration, often providing alternative proofs of known results. This work also includes the application of probability theory to games of chance and his introduction of the theorem known asthe law of large numbers.law of large numbers BaselBasel, SwitzerlandSwitzerland

5. Nicolaus Bernoulli (1623-1708) Jakob BernoulliJakob Bernoulli (1654–1705)Nicolaus Bernoulli (1662–1716) Johann BernoulliJohann Bernoulli (1667–1748) Nicolaus I BernoulliNicolaus I Bernoulli (1687-1759) Nicolaus II BernoulliNicolaus II Bernoulli (1695–1726) Daniel BernoulliDaniel Bernoulli (1700–1782) Johann II BernoulliJohann II Bernoulli (1710–1790) Johann III BernoulliJohann III Bernoulli (1744–1807) Daniel II Bernoulli (1751–1834) Jakob II BernoulliJakob II Bernoulli (1759–1789)

6. Abraham de Moivre France 26 May26 May 1667 – 27 November 1754166727 November1754 De Moivre wrote a book on probability theory,probability theory entitled The Doctrine of Chances. It was saidThe Doctrine of Chances that his book was highly prized by gamblers. It is reported in all seriousness that de Moivre correctly predicted the day of his own death. Noting that he was sleeping 15 minutes longer each day, De Moivre surmised that he would die on the day he would sleep for 24 hours. A simple mathematical calculation quickly yielded the date, 27 November 1754. He did indeed pass away27 November1754on that day.

7. Pierre-Simon Laplace 23 March 1749 - 5 March 1827 French In 1812, Laplace issued his Théorie analytique des probabilités in which he laid down many fundamental results in statistics.statistics

8. Johann Carl Friedrich Gauss 30 April30 April 1777 – 23 February 1855177723 February1855 Germany The normal distribution, also called the Gaussian distribution,

10. The normal distribution was first introduced by Abraham de MoivreAbraham de Moivre in an article in 1733, which was reprinted in the second edition of his The Doctrine of ChancesThe Doctrine of Chances, 1738 in the context of approximating certain binomial distributionsbinomial distributions for large n. His result was extended by LaplaceLaplace in his book Analytical Theory of Probabilities (1812), and is now called theAnalytical Theory of Probabilities theorem of de Moivre-Laplacetheorem of de Moivre-Laplace. Laplace used the normal distribution in the analysis of errors of experiments.analysis of errors

11. Its usefulness, however, became truly apparent only in 1809, when the famous German mathematician K.F. Gauss used it as an integral part of his approach to prediction the location of astronomical entities. As a result, it became common after this time to call it the Gaussian distribution.

12. During the mid to late nineteenth century, however, most statisticians started to believe that the majority of data sets would have histograms conforming to the Gaussian bell-shaped form. Indeed, it came to be accepted that it was “normal” for any well-behaved data set to follow this curve. As a result, following the lead of the British statistician Karl Pearson, people began referring to the Gaussian curve to calling it simply the normal curve.

13. The name "bell curve" goes back to Esprit Jouffret who first usedEsprit Jouffret the term "bell surface" in 1872 for a bivariate normal with independentbivariate normal components. The name "normal distribution" was coined independently by Charles S. Peirce, Francis Galton and Wilhelm Lexis around 1875.Charles S. PeirceFrancis GaltonWilhelm Lexis

15. Andrey Nikolaevich Kolmogorov 25 April 1903 -- 20 Oct 1987 Moscow, Russia His monograph on probability theory Grundbegriffe der Wahrscheinlichkeitsrechnung published in 1933 built up probability theory in a rigorous way from fundamental axioms in a way comparable with Euclid's treatment of geometry.

16. Buffon's Needle Problem the French naturalist Buffon in 1733

17. Buffon's needle problem asks to find the probability that a needle of length will land on a line, given a floor with equally spaced parallel lines a distanceparallellines apart. The problem was first posed by the French naturalist Buffon in 1733 (Buffon 1733, pp. 43-45), and reproduced with solution by Buffon in 1777 Several attempts have been made to experimentally determine by needle-tossing. π

18. Thomas Bayes 1702 - 1761 London, England Bayes' theorem gives the rule for updating belief in a Hypothesis H (i.e. the probability of H) given additional evidence E, and background information (context) I p(H|E,I) = p(H|I)*p(E|H,I)/p(E|I) [Bayes Rule] p(H|E,I), is called the posterior probability, The p(H|I) is just the prior probability of H given I alone

19. Bayes' theorem is particularly useful for inferring causes from their effects since it is often fairly easy to discern the probability of an effect given the presence or absence of a putative cause. For instance, physicians often screen for diseases of known prevalence using diagnostic tests of recognized sensitivity and specificity. The sensitivity of a test, its "true positive" rate, is the fraction of times that patients with the disease test positive for it. The test's specificity, its "true negative" rate, is the proportion of healthy patients who test negative. one can use to determine the probability of disease given a positive test.

20. The essence of the Bayesian approach is to provide a mathematical rule explaining how you should change your existing beliefs in the light of new evidence. In other words, it allows scientists to combine new data with their existing knowledge or expertise. The canonical example is to imagine that a precocious newborn observes his first sunset, and wonders whether the sun will rise again or not.