Class Probabilities and Statistics

Provides a wide range of basic mathematical knowledge, skills and tools in the area of Probability and Statistics essential for Engineering studies.

Descriptive statistics: main measures of central, non-central tendency and of dispersion. Linear correlation and regression.

Random experience. Event. Sample space. Algebra of events. Probability concepts (Laplace and Kolmogorov). Conditional probability. Independence.

Discrete and continuous random variables. Probability and distribution functions. Mathematical expectation: mean, variance, and standard deviation.

Discrete distributions. Uniform, Bernoulli, Binomial, and Poisson distribution.

Continuous distributions. Normal, Chi-square, t-student, and exponential distribution.

Statistical inference. Sampling distributions. Central limit theorem.

Range estimation. Confidence interval for the mean, known and unknown variance, large and small sample. Intervals for the proportion.

Tests of Hypotheses for the mean and the proportion.

A series of exercises will be proposed aiming at consolidating knowledge and stimulating the ability to solve problems. The evaluation of the subject, expressed on a scale of 0 to 20 values, will be done at various times including 2 midterms (40%+50%) and individual work to be developed outside the classroom (10%). If the weighted average of these moments is equal to or greater than 9.5, the student will be successful in the course, otherwise the student will be able to take a global frequency (90%) to which the mentioned 10% will be added. In the final exam (100%) the student will be able to improve the grade. The minimum passing grade in this assessment is also 9.5. Assessment criteria are explained at the beginning of the semester.

Murteira, B. (2012), Probabilidades e Estatística, MacGraw-Hill.

Murteira, B. (2007), Introdução à Estatística, MacGraw-Hill.

Pedrosa, A.C., Gama, S.M. (2018), Introdução computacional à Probabilidade e Estatística, Porto Editora