Elements of Probability and Statistics
Cod: 21037
Department: DCET
ECTS: 6
Scientific area: Mathematics
Total working hours: 156
Total contact time: 26
In this curricular unit, the basic concepts of probability and statistical theory are introduced. Starting with a reference to some of the methods of description of the data and observations, it continues with the concept of uncertainty associated with the events and the most fundamental concepts of probability theory. Random variables are introduced, the notions of discrete and continuous random variables, and some of the most important distribution laws and theoretical results.
1. Descriptive statistics
2. Probabilities
3. Discrete Random Variables
4. Continuous Random Variables
By completing this course the student should be able to:
• Translate into probability theory language problems related to uncertainty scenarios;
• Use concepts and rules of probability calculus in random variables;
• Apply in practical situations some of the most important distribution laws;
• Apply theoretical results for sums of random variables.
• Description of data and observations.
• Events and sets. Probability theory. Conditional probability.
• Unidimensional discrete and continuous random variables. Probability and Density functions. Distribution function. Moments of random variables.
• Discrete Distribution laws: discrete - uniform, Bernoulli, binomial, geometric, hypergeometric, Poisson.
• Continuous Distribution Laws:  uniform, normal, exponential, gamma, chi-square. Sums of random variables.
• Central Limit Theorem and its corollaries.
• Relation between different random variables: covariance and correlation. Bivariate joint distributions.