


Politecnico di Torino  
Academic Year 2009/10  
01BXTDR, 01BXTAX, 01BXTJA Probability and statistics 

1st degree and Bachelorlevel of the Bologna process in Mechanical Engineering  Vercelli 1st degree and Bachelorlevel of the Bologna process in Civil Engineering  Vercelli 1st degree and Bachelorlevel of the Bologna process in Electronic And Computer Engineering  Vercelli 





Objectives of the course
Provide basic knowledge on probability theory and statistics.

Expected skills
To be able to solve problems of probability theory making use of the concepts of discrete and continuous random variables, joint and conditional probability. Computing generating functions of common discrete and continuous probability distributions: binomial, Poisson, exponential. Extracting statistical properties from a dataset. Knowning the typical graphical representations of the statistical properties of a dataset. Performing hypothesis testing.

Prerequisites
Calculus I, II

Syllabus
Method of least squares. Covariance, correlation coefficient. Probability axioms: positivity, normalization, summability. Classical probability.
Discrete probability, combinatorial calculus. Conditional probability. Bayes' formula. Independent events. Discrete random variables. Probability distribution of a random variable. Probability distribution of Bernoulli's, binomial, geometric random variables. Expectation value, variance. Variance and covariance. Chebichev inequality. Expectation value and variance of the sample average, law of large numbers. Poisson's law of rare events. Generating function of the moments. Continuous random variables. Jont and marginal probability distribution. Sum of independent random variables. The exponential and Gamma laws. Sum of normal random variables. Central limit theorem. Normality test, normal probability plot. Confidence intervals for mean and variance, chisquare and Student laws. Hypothesis testing for the mean with known and unknown variance. 
Laboratories and/or exercises
Exercises about the arguments of the course are discussed and solved in the class.

Bibliography
Devore, 'Probability and Statistics for Engineering and the Sciences', Duxbury Press

Revisions / Exam
The exam consists of written exercises and questions about the arguments discussed in the course.

