Probability, First Course

Aim

After completing the course, the student will be able to:

• identify experimental situations where random factors can affect the result, as well as set up relevant probability-theoretic models for such experiments.
• explain basic probability theoretical concepts and laws, e.g. random variable, distribution function and the law of total probability.
• calculate important quantities in probability theory models, e.g. probabilities, expected values ​​and variances, and clearly report these calculations.
• have achieved the knowledge and skills required for a basic course in statistics.

Content

Sample space, events and probabilities. Combinatorics. Conditional probabilities and independent events. Discrete and continuous random variables. Distribution functions, probability mass functions, probability density functions. Conditional distributions and independent random variables. Functions of random variables. Expectation, variance, standard deviation, covariance, correlation coefficient. Particular distributions, e.g., Gaussian, exponential, uniform, binomial and Poisson distributions. Law of large numbers and the central limit theorem. The Poisson process.