Entry requirements

Several Variable Calculus M.

Learning outcomes

On completion of the course, the student should be able to

• account for the axiomatic basis of the probability theory;
• carry out probability calculations by means of combinatorial principles and be able to use methods for independent events;
• account for the concepts of stochastic variable and expectation and be able to calculate probabilities, expectations and variance for given distributions;
• elementary account for the most common probability distributions;
• handle conditioned probabilities, distributions and expectations as well as moment generating functions;
• apply the law of large numbers and the central limit theorem;
• account for probabilistic models within different application fields.

Content

Combinatorics. The probability concept. Calculation of probabilities. Stochastic variable. Probability distributions. Independent and conditioned distributions. Expectation and variance. Conditioned expectations. Moment generating function. The central limit theorem. The law of large numbers. Practical examples of design of probability models.

Instruction

Lectures, teaching sessions and calculation exercises.

Assessment

Written examination at the end of the course combined with written assignments during the course according to instructions delivered at course start.

Other directives

The course can not be included in higher education qualification together with any of the courses Probability and statistics (1MS005) or Probability Theory (1MS006).