MA464/564 Theory of probability, distributed Text material

This course in probability theory was given at the univerity of Arizona in the spring semester 1997.
Most of the distributed text material is available in the form of PS files.

    INTRODUCTION

  1. Bertrands paradox (GIF)
  2. Petersburg Casino (GIF)
  3. Coins (Link)
  4. Foundation of probability (PS File)
  5. Cars, Goats, Boys and Girls (Link)
  6. Bertrand/Car-Goat/Petersburg (PS File)
  7. Two controversal problems (PS File)

    COMBINATORICS

  8. Basic combinatorics (PS File)

    DISCRETE DISTRIBUTIONS

  9. Small probabilities (PS File)
  10. Discrete distributions (PS File)
  11. Discrete distrib. (II) (PS File)
  12. A sailor, Euler and a devilish stair
  13. Expectation and Variance (PS File)
  14. Probability gen. funct. (PS File)

    SOME NICE MATH

  1. Weierstrass theorem
  2. Banach-Tarski paradox
  3. Theorem of Caratheodory.
  4. The Lebesgue integral.

    CONTINUOUS DISTRIBUTIONS

  5. Some continuous distributions
  6. Random vectors (I)
  7. Random vectors (II)
  8. A stronger central limit theorem
  9. Some inequalities
  10. Derivation of Stirlings formula
  11. Characteristic functions
  12. Convergence of random variables

    STOCHASTIC PROCESSES

  13. Recurrence of random walks
  14. One dim random walk (1)
  15. Borel-Cantelli lemma
  16. One dim random walk (2)
  17. Poisson distribution
  18. Summary and outlook
  19. Brownian motion
  20. Black-Scholes formula
  21. Feynman-Kac formula

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