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Probability basics

Probability basics - 1 Axi oms of pr oba bi l i ty 1.1 I...

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    1. Axioms of probability
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p2. 1.1 Introduction Luca Paccioli(1445-1514)  Italian     (studies of chances of events) Niccolo Tartaglia(1499-1557) Girolamo Cardano(1501-1576) Galileo Galielei(1564-1642) Blaise Pascal(1623-1662) French           Pierre de Fermat(1601-1665) 1655 Christian Huygens(1629-1695)  Dutch            first book “On Calculations in Games of Chance) James Bernoulli(1654-1705) Abraham de Moivre(1667-1754)
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p3. I ntroduction Pierre-Simon Laplace(1749-1827) Simeon Denis Poisson(1781-1840) Karl Friedrich Gauss(1777-1855) Pafnuty Chebyshev(1821-1894)  Russian Andrei Markov(1856-1922) Aleksandr Lyapunov(1857-1918) 1900 David Hilbert(1862-1943)  pointed out the problem  of the axiomatic treatment of the theory of  probability
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p4. I ntroduction Emile Borel(1871-1956) Serge Bernstein(1880-1968) Richard von Mises(1883-1953) * 1933 Andrei Kolmogorov(1903-1087)  Russian successfully axiomatized the theory of probability
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p5. 1.2 Sample space and events Experiment  (eg. Tossing a die) Outcome (sample point) Sample space ={all outcomes} Event : subset of sample space   Ex1.1  tossing a coin once     sample space S = {H, T} Ex1.2  flipping a coin and tossing a die if T                or flipping a coin again if   H                S={T1,T2,T3,T4,T5,T6,HT,HH}
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