Fundamentals of Probabilistics Methods

This cours is intended as an basic introduction to the theory of probability for students in engineering. The cours consists of 15 two-hours lectures during which the presented  topics are the following:

1. Basic Probability Concept: the notion of random experiment, outcome, sample space, event, the collection of events, probability measure, the notion of Probability Kolmogorov Model.
2. The notion of probability distribution:  discrete distribution, "step" function as cummulative distribution function, dicrete random variable, The Bernoulli and Binomial distribution, the Poisson distribution, other discrete distributions, continuous probability distribution, density probability function, continuous random variable, Gaussian random variable, uniform random variable, exponential random variable.
3. The parameters of random variables: mathematical expectation, variance and probability interpretation.
4.   The concept of Limit Theorem: the DeMoivre-Laplace Limit Theorem, the Strong Law of Large Numbers, the Central Limit Theorem.
5. Jointly distributed random variables: the notion of random vector, joint distribution function, marginal distribution, sums of independent random variables.

REFERENCES

1. R. Rębowski, Podstawy metod probabilistycznych, Seria Wydawnicza PWSZ im. Witelona w Legnicy, 2006.
2. R. Rębowski, J. Płaskonka, Zbiór zadań z metod probabilistycznych, Seria Wydawnicza PWSZ im. Witelona w Legnicy, 2008.
3. S. Ross, A First Course in Probability, 8 ed., Prentice Hall 2010.
4. S. Ross, Solutions Manual A First Course in probability 7 ed. Prentice Hall 2010.
5. R.B. Schinazi, Probability with Statistical Applications, Birkhauser, Springer Science, 2012.

List of problems    first  second