Upon successful completion of the course, the students should:
- have a general overview of statistical methods
- know the principle definitions, fundamental theorems, and important relationships in statistics
- understand how random variables and stochastic processes can be described and analyzed
- know the most important distributions and their characteristics
- be able to understand, analyze, and solve typical problems in statistics
- understand the role of probability theory as well as the concept of random variables and stochastic processes in information and communication technology
- have competence in applying statistical methods to solve basic problems in information and communication technology
Probability Theory: Meaning and definition of probability, axioms of probability, probability space, conditional and total probability, Bayes' theorem, independence repeated trials, definition of random variables, cumulative distribution function, probability density function, important types of distributions (uniform, Gaussian, exponential, Rayleigh, Rice, Nakagami, lognormal, Poisson, Bernoulli, binomial), functions of random variables, concept of transformation of random variables, Chebyshev and Markov inequalities, characteristic functions, two random variables, joint distribution and joint density, joint moments, joint characteristic function, conditional probability, independence of random variables, sums of random variables, sample mean and sample variance, laws of large numbers, central limit theorems for sums and products, hypothesis testing.
Stochastic Processes: Definition of stochastic processes, statistics of stochastic processes, strict-sense stationary and wide-sense stationary stochastic processes, ergodic processes, autocorrelation and cross-correlation functions, Wiener-Khinchin theorem, power spectral density, cross-power spectral density, linear time invariant systems with stochastic inputs, Wiener-Lee relation, white noise, system identification, matched filter.
The course comprises of lectures and exercises. The lecture notes and exercise problems will be given in the LMS at the start of the semester. It is expected that the students prepare in advance of the lecture and exercise classes. During the exercise class, the lecturer presents the solution on the blackboard and gives guidance to the students. In addition, reference solutions to the exercises are presented in the LMS.
The work load for the average student is approximately 200 hours.
Faculty of Engineering and Science