Ingegneria Meccanica | STATISTICS

cod. 0612300051

STATISTICS

	0612300051
	DIPARTIMENTO DI INGEGNERIA INDUSTRIALE
	EQF6
	MECHANICAL ENGINEERING
	2022/2023

PERCORSO IN COMMON

	YEAR OF COURSE 3
	YEAR OF DIDACTIC SYSTEM 2018
	AUTUMN SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	SECS-S/02	6	60	LESSONS	OPTIONAL SUBJECTS

EXAMS

	Exam	Date	Session
	STATISTICA PER L'INGEGNERIA DI PROCESSO	20/04/2023 - 14:00	SESSIONE ORDINARIA
	STATISTICA PER L'INGEGNERIA DI PROCESSO	20/04/2023 - 14:00	SESSIONE DI RECUPERO

	Objectives
	Knowledge and understanding Definitions of random variable and main distributions and their moments; event probability assessment; statistical inference and decision; analysis of variance and linear regression analysis. Applied knowledge and understanding - engineering analysis Ability to solve problems involving the evaluation of probability of events, the estimation of unknown parameters and the verification of hypotheses concerning non-deterministic phenomena, the identification and the application of simple empirical models for the quantitative analysis of physical and / or technological phenomena. Applied knowledge and understanding - engineering design In a design context, find the variables for which you need to use the tools statistical analysis and apply these tools. Independence of judgment - engineering practice Ability to apply methods and tools to analyze the effect of different factors on a phenomenon of interest and make quantitative comparisons between them Ability to learn - ability to investigate Ability to use methods and tools to plan data collection in order to allow objective analysis of the problem treated. Transversal skills - communication skills Knowing how to present both orally and in writing a topic related to the probabilistic evaluation of a random phenomenon. Knowing how to present the topics of statistical data analysis in a correct and exhaustive way. Transversal skills - ability to learn Knowing how to apply the knowledge acquired to contexts different from those presented during the course. Knowing use different sources for in-depth study of the methodologies introduced in the course.

Knowledge and understanding
Definitions of random variable and main distributions and their moments; event probability assessment;
statistical inference and decision; analysis of variance and linear regression analysis.
Applied knowledge and understanding - engineering analysis
Ability to solve problems involving the evaluation of probability of events, the estimation of unknown parameters and the verification of hypotheses concerning non-deterministic phenomena, the identification and the application of simple empirical models for the quantitative analysis of physical and / or technological phenomena.
Applied knowledge and understanding - engineering design
In a design context, find the variables for which you need to use the tools statistical analysis and apply these tools.
Independence of judgment - engineering practice
Ability to apply methods and tools to analyze the effect of different factors on a phenomenon of interest
and make quantitative comparisons between them
Ability to learn - ability to investigate
Ability to use methods and tools to plan data collection in order to allow objective analysis
of the problem treated.
Transversal skills - communication skills
Knowing how to present both orally and in writing a topic related to the probabilistic evaluation of a
random phenomenon. Knowing how to present the topics of statistical data analysis in a correct and exhaustive way.
Transversal skills - ability to learn
Knowing how to apply the knowledge acquired to contexts different from those presented during the course. Knowing use different sources for in-depth study of the methodologies introduced in the course.

	Prerequisites
	FOR THE SUCCESSFUL ACHIEVEMENT OF THE OBJECTIVES, A SUITABLE KNOWLEDGE OF BASIC MATHEMATICS IS REQUIRED, AS GUARANTEED BY THE MATHEMATICS I COURSE.

	Contents
	•ELEMENTS OF PROBABILITY THEORY AND COMBINATORIAL CALCULUS. AXIOMS OF PROBABILITY. CONDITIONAL PROBABILITY AND INDEPENDENCE. TOTAL PROBABILITY THEOREM. BAYES THEOREM. COMBINATORIAL CALCULUS. (HOURS: LESSONS/EXERCISES/LABORATORY 4/2/-) •RANDOM VARIABLES. DEFINITION OF A RANDOM VARIABLE (R.V.) AND ITS PROBABILITY DISTRIBUTION AND PROBABILITY DENSITY FUNCTION. MEAN AND VARIANCE OF A R.V.. FUNCTIONS OF A RANDOM VARIABLE. COUPLES OF R.V.’S AND THEIR JOINT AND MARGINAL DISTRIBUTIONS. COVARIANCE. DISTRIBUTIONS OF DISCRETE AND CONTINUOUS R.V.’S OF COMMON USE (HOURS 7/4/-) •DESCRIPTIVE STATISTICS. POPULATION AND SAMPLE. RANDOM SAMPLE. FREQUENCY AND RELATIVE FREQUENCY DISTRIBUTION FOR DISCRETE AND CONTINUOUS VARIABLES. HISTOGRAMS. STATISTICAL POSITION INDEXES: SAMPLE MEAN, MEDIAN, MODE. STATISTICAL DISPERSION INDEXES: SAMPLE VARIANCE, SAMPLE STANDARD DEVIATION, RANGE. (HOURS 3/1/-) •ELEMENTS OF INFERENTIAL STATISTICS. BASIC CONCEPTS OF INDUCTIVE REASONING. POINT AND INTERVAL ESTIMATION OF POPULATION PARAMETERS. HYPOTHESIS TESTING. TYPE I AND TYPE II RISKS. CONFIDENCE INTERVAL AND HYPOTHESIS TESTING FOR THE MEAN OF A NORMAL POPULATION IN CASE OF BOTH KNOWN AND UNKNOWN VARIANCE. STUDENT T DISTRIBUTION. CONFIDENCE INTERVAL AND HYPOTHESIS TESTING FOR THE VARIANCE OF A NORMAL POPULATION. CHI-SQUARED DISTRIBUTION. (HOURS 10/5/-) •DESIGN OF EXPERIMENTS(DOE) AND ANALYSIS OF VARIANCE (ANOVA). BASIC CONCEPTS AND DEFINITIONS OF DOE. COMPLETELY RANDOMIZED DESIGN. RANDOMIZED BLOCK DESIGN. LATIN SQUARES. FULL FACTORIAL DESIGN. PARTITION OF TOTAL VARIABILITY. ONE WAY AND TWO WAY ANOVA. RESIDUAL ANALYSIS. (HOURS 10/5/-) •LINEAR REGRESSION ANALYSIS. ASSOCIATION AMONG VARIABLES: CORRELATION COEFFICIENT. SIMPLE LINEAR REGRESSION MODEL. LEAST SQUARES ESTIMATION METHOD. GOODNESS-OF-FIT MEASURES: COEFFICIENT OF DETERMINATION. MULTIPLE LINEAR REGRESSION. STEPWISE PROCEDURE FOR CHOOSING THE BEST REGRESSION MODEL. (HOURS 6/3/0)

Contents

•ELEMENTS OF PROBABILITY THEORY AND COMBINATORIAL CALCULUS. AXIOMS OF PROBABILITY. CONDITIONAL PROBABILITY AND INDEPENDENCE. TOTAL PROBABILITY THEOREM. BAYES THEOREM. COMBINATORIAL CALCULUS. (HOURS: LESSONS/EXERCISES/LABORATORY 4/2/-)
•RANDOM VARIABLES. DEFINITION OF A RANDOM VARIABLE (R.V.) AND ITS PROBABILITY DISTRIBUTION AND PROBABILITY DENSITY FUNCTION. MEAN AND VARIANCE OF A R.V.. FUNCTIONS OF A RANDOM VARIABLE. COUPLES OF R.V.’S AND THEIR JOINT AND MARGINAL DISTRIBUTIONS. COVARIANCE. DISTRIBUTIONS OF DISCRETE AND CONTINUOUS R.V.’S OF COMMON USE (HOURS 7/4/-)
•DESCRIPTIVE STATISTICS. POPULATION AND SAMPLE. RANDOM SAMPLE. FREQUENCY AND RELATIVE FREQUENCY DISTRIBUTION FOR DISCRETE AND CONTINUOUS VARIABLES. HISTOGRAMS. STATISTICAL POSITION INDEXES: SAMPLE MEAN, MEDIAN, MODE. STATISTICAL DISPERSION INDEXES: SAMPLE VARIANCE, SAMPLE STANDARD DEVIATION, RANGE. (HOURS 3/1/-)
•ELEMENTS OF INFERENTIAL STATISTICS. BASIC CONCEPTS OF INDUCTIVE REASONING. POINT AND INTERVAL ESTIMATION OF POPULATION PARAMETERS. HYPOTHESIS TESTING. TYPE I AND TYPE II RISKS. CONFIDENCE INTERVAL AND HYPOTHESIS TESTING FOR THE MEAN OF A NORMAL POPULATION IN CASE OF BOTH KNOWN AND UNKNOWN VARIANCE. STUDENT T DISTRIBUTION. CONFIDENCE INTERVAL AND HYPOTHESIS TESTING FOR THE VARIANCE OF A NORMAL POPULATION. CHI-SQUARED DISTRIBUTION. (HOURS 10/5/-)
•DESIGN OF EXPERIMENTS(DOE) AND ANALYSIS OF VARIANCE (ANOVA). BASIC CONCEPTS AND DEFINITIONS OF DOE. COMPLETELY RANDOMIZED DESIGN. RANDOMIZED BLOCK DESIGN. LATIN SQUARES. FULL FACTORIAL DESIGN. PARTITION OF TOTAL VARIABILITY. ONE WAY AND TWO WAY ANOVA. RESIDUAL ANALYSIS. (HOURS 10/5/-)
•LINEAR REGRESSION ANALYSIS. ASSOCIATION AMONG VARIABLES: CORRELATION COEFFICIENT. SIMPLE LINEAR REGRESSION MODEL. LEAST SQUARES ESTIMATION METHOD. GOODNESS-OF-FIT MEASURES: COEFFICIENT OF DETERMINATION. MULTIPLE LINEAR REGRESSION. STEPWISE PROCEDURE FOR CHOOSING THE BEST REGRESSION MODEL. (HOURS 6/3/0)

	Teaching Methods
	The course consists of in front lessons (40 h) and exercizes (20 h) for a total amount of 60 hours which are worth 6 credits. Attendance at the lectures is strongly recommended.

	Verification of learning
	THE GOAL OF THE FINAL EXAM IS THE EVALUATION OF THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE COURSE, THE ABILITY TO APPLY THAT KNOWLEDGE TO SOLVE PROBLEMS ON PROBABILITY, TO ESTIMATE UNKNOWN MODEL PARAMETERS, TO MAKE DECISION ON THE BASIS OF HYPOTHESES TESTING, TO STUDY THE EFFECTS OF PRIMARY FACTORS ON PHYSICAL AND/OR TECHNOLOGICAL PHENOMENA AND TO ASSESS SIMPLE EMPIRICAL MODELS FOR THEM. FURTHERMORE, THE PERSONAL JUDGEMENT, THE COMMUNICATION SKILLS AND THE LEARNING ABILITIES ARE ALSO EVALUATED. THE FINAL EXAM CONSISTS OF A WRITTEN TEST WHICH AIMS TO ASSESS THE ABILITY TO SOLVE PROBLEMS ABOUT THE TOPICS PRESENTED DURING THE COURSE, SUCH AS: 1) BASIC PROBABILITY EVALUATIONS; 2) BASIC STATISTICAL INFERENCE AND DECISION MAKING; 3) BASIC ANOVA AND LINEAR REGRESSION ANALYSES. THE WRITTEN TEST IS EVALUATED ON THE BASIS OF THE CORRECTNESS OF THE APPROACH AND THE RESULTS ACCORDING TO A SCORE, EXPRESSED OUT OF THIRTY. THE “INSUFFICIENT” SCORE IMPLIES THE WRITTEN TEST REPETITION. AFTER THE WRITTEN TEST, STUDENTS MAY ASK TO DO AN ORAL INTERVIEW, TOO. THIS INTERVIEW WILL BE ADDRESSED TO VERIFY THE ACQUIRED KNOWLEDGE ALSO ON THE TOPICS NOT COVERED BY THE WRITTEN TEST. IN SUCH CASE, THE WRITTEN TEST WILL CONTRIBUTE FOR 60% TO THE FINAL SCORE, WHILE THE ORAL INTERVIEW FOR 40%. AN ORAL INTERVIEW THAT IS NOT CONSIDERED SUFFICIENT IMPLIES THE REPETITION OF THE WRITTEN TEST, TOO. The sufficiency is obtained if the candidate demonstrates the ability to select the methods to be used, to write correctly the model equations and at least to select the correct path to their solution. The excellence is obtained when the candidate is able to face out successfully even aspects of the topic not analyzed during the course. The final grade depends from the level of exposition and from the confidence shown with the course’s topics, and with the methods, the uses of which have been shown during the course.

Verification of learning

THE GOAL OF THE FINAL EXAM IS THE EVALUATION OF THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE COURSE, THE ABILITY TO APPLY THAT KNOWLEDGE TO SOLVE PROBLEMS ON PROBABILITY, TO ESTIMATE UNKNOWN MODEL PARAMETERS, TO MAKE DECISION ON THE BASIS OF HYPOTHESES TESTING, TO STUDY THE EFFECTS OF PRIMARY FACTORS ON PHYSICAL AND/OR TECHNOLOGICAL PHENOMENA AND TO ASSESS SIMPLE EMPIRICAL MODELS FOR THEM. FURTHERMORE, THE PERSONAL JUDGEMENT, THE COMMUNICATION SKILLS AND THE LEARNING ABILITIES ARE ALSO EVALUATED.

THE FINAL EXAM CONSISTS OF A WRITTEN TEST WHICH AIMS TO ASSESS THE ABILITY TO SOLVE PROBLEMS ABOUT THE TOPICS PRESENTED DURING THE COURSE, SUCH AS: 1) BASIC PROBABILITY EVALUATIONS; 2) BASIC STATISTICAL INFERENCE AND DECISION MAKING; 3) BASIC ANOVA AND LINEAR REGRESSION ANALYSES. THE WRITTEN TEST IS EVALUATED ON THE BASIS OF THE CORRECTNESS OF THE APPROACH AND THE RESULTS ACCORDING TO A SCORE, EXPRESSED OUT OF THIRTY. THE “INSUFFICIENT” SCORE IMPLIES THE WRITTEN TEST REPETITION.

AFTER THE WRITTEN TEST, STUDENTS MAY ASK TO DO AN ORAL INTERVIEW, TOO. THIS INTERVIEW WILL BE ADDRESSED TO VERIFY THE ACQUIRED KNOWLEDGE ALSO ON THE TOPICS NOT COVERED BY THE WRITTEN TEST. IN SUCH CASE, THE WRITTEN TEST WILL CONTRIBUTE FOR 60% TO THE FINAL SCORE, WHILE THE ORAL INTERVIEW FOR 40%. AN ORAL INTERVIEW THAT IS NOT CONSIDERED SUFFICIENT IMPLIES THE REPETITION OF THE WRITTEN TEST, TOO.

The sufficiency is obtained if the candidate demonstrates the ability to select the methods to be used, to write correctly the model equations and at least to select the correct path to their solution.
The excellence is obtained when the candidate is able to face out successfully even aspects of the topic not analyzed during the course.
The final grade depends from the level of exposition and from the confidence shown with the course’s topics, and with the methods, the uses of which have been shown during the course.

	Texts
	LECTURE NOTES ON PROBABILITY AND COMBINATORIAL CALCULUS (IN ITALIAN). S. M. ROSS, PROBABILITÀ E STATISTICA PER L’INGEGNERIA E LE SCIENZE, APOGEO. COMPLEMENTARY BOOKS