Probability theory 1984/85.

For 4th year mathematics students. Official name: Algebra superiore.

THE CONCEPT OF RANDOM VARIABLE What is a random variable? Categories and functors Lattices and Boolean algebras The algebra of imaginations THEORY OF PROBABILITY The space of events Algebras and sigma-algebras of sets Probability measures Independent events Bernoulli process Conditional probability Kolmogorov's concept of random variable More on the Bernoulli process Random walk 2-dimensional distributions Mean value of discrete random variables Real valued random variables Basic measure systems Monotone functions and functions of bounded variation Integration Riemann-Stieltjes integral Normal distribution Exponential distribution Poisson distribution Poisson process EXAMPLES FROM STATISTICS Chebyshev's inequality Sample mean and sample variance Confidence intervals