Unit STATISTICS AND OPERATIONAL RESEARCH
 Course
 Mechanical engineering
 Studyunit Code
 70A00209
 Curriculum
 Gestionale
 CFU
 9
 Course Regulation
 Coorte 2020
 Offered
 2021/22
 Type of studyunit
 Type of learning activities
 Attività formativa integrata
OPERATION RESEARCH
Code  70097005 

CFU  5 
Teacher  Giuseppe Saccomandi 
Teachers 

Hours 

Learning activities  Base 
Area  Matematica, informatica e statistica 
Academic discipline  MAT/09 
Type of studyunit  
Language of instruction  Italiano but with online lectures on English 
Contents  Basic Methods of Operation Research 
Reference texts  https://www.youtube.com/yongwang 
Educational objectives  The ability to solve some linear optimisation problem with and without software tools. 
Prerequisites  Calculus 
Teaching methods  Classical 
Other information  None 
Learning verification modality  Oral and written examination 
Extended program  o Linear Programming o Simplex Algorithm and Goal Programming o Sensitivity Analysis and Duality o Transportation, Assignment, and Transshipment Problems o Network Models o Integer Programming o Nonlinear Programming o Decision Making under Uncertainty o Game Theory o Inventory Theory o Markov Chains o Dynamic Programming o Queuing Theory 
STATISTICS
Code  70026681 

CFU  4 
Teacher  Paolo Carbone 
Teachers 

Hours 

Learning activities  Affine/integrativa 
Area  Attività formative affini o integrative 
Academic discipline  SECSS/02 
Type of studyunit  
Language of instruction  Italian 
Contents  Introduction to probability theory: continuous, discrete and mixed random variables. Probability density functions. Probability distribution functions. Joint random variables. Introduction to stochastic processes: definitions, autocorrelation and autocovariance functions. Fundamentals of stochastic processes. 
Reference texts  Roy. D. Yates, David J. Goodman, Probability and Stochastic Processes, John Wiley & Sons Inc; 2nd International Edition, 2004. Handouts by the instructor. 
Educational objectives  The objective of this module is to provide the students with the knowledge to correctly apply probability theory and measurement theory. At the end of this class the student will have learned:  the concept of continuous and discrete random variable and its PDF and CDF  the concept of function of a random variable  the concept of joint random variables and vector of random variables  the concept of function of two random variables  the concept of stochastic process and of its general properties Moreover, he will be able to:  solve exercises that require modeling using discrete, continuous and mixed random variables  solve exercises using the concept of stochastic process 
Prerequisites  Calculus I is mandatory. Students must also be able to perform simple mathematical modeling in two dimensions and capable to solve simple double integrals. 
Teaching methods  Frontal lectures at the blackboard. Students are expected to provide active participation and show autonomous study capabilities. Proficiency in solving exercises can only be developed by complementing attendance of lectures with dedicated sessions in the solution of exercises at home. 
Other information  Information about available services for people with disabilities and/or with learning disabilities, see: http://www.unipg.it/disabilitaedsa 
Learning verification modality  Written and oral tests. The written test requires solving two exercises (7 and 8 points each) and in answering 15 quizzes with 4 possible answers, of which only one is the correct one. To each correct quiz answer 1 point is assigned. Wrong answers results in minus half a point. The oral examination covers all course content program and consists both in questions about the theory and in the solution of exercises. Its lenght is about 2025 minutes. The final grade is based on both grades in the written and oral examinations. 
Extended program  Set theory. Sample spaces and random events. How to assign probabilities: classical, empirical and subjective approach. Conditional probability. Total probability theorem. Bayes theorem. Combinatorial calculus: permutations, dispositions, combinations. Random variables. Cumulative3 distribution function. Probability density function. Discrete random variables: Bernoulli, geometrical, binomial, Pascal, uniform discrete. Mode, median, expected value. Transformed random variables. Expected value of a transformed random variable. Variance and standard deviation. Central and noncentral moments. Conditional mass probability. Continuous random variables. Cumulative and density functions. Expected value. Probability models: uniform, exponential, Gaussian. Mixed random variables. Transformed continuous random variables. Conditional continuous random variables. Couples of random variables. Marginal probability density functions. Transformation of two random variables. Rayleigh and Rice probability models. Orthogonal random variables. Correlation, covariance. Correlation coefficient. Conditioning two random variables. Random vectors. Gaussian random vectors. Central limit theorem. DeMoivre Laplace formula. Introduction to stochastic processes. Moments. Widesense and strictsense stationary random processes. Ergodic processes. 