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