Computer science | PROBABILITY AND MATHEMATICAL STATISTICS

cod. 0512100009

PROBABILITY AND MATHEMATICAL STATISTICS

	0512100009
	DIPARTIMENTO DI INFORMATICA

	COMPUTER SCIENCE
	2013/2014

CURRICULUM METODOLOGICO

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2008
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/06	6	48	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

	Objectives
	1. KNOWLEDGE AND UNDERSTANDING THOROUGH UNDERSTANDING OF THE BASIC TOPICS OF PROBABILITY AND MATHEMATICAL STATISTICS. ABILITY TO IDENTIFY A PROBABILISTIC MODEL AND TO UNDERSTAND ITS MAIN FEATURES. 2. APPLYING KNOWLEDGE AND UNDERSTANDING INDUCTIVE AND DEDUCTIVE REASONING SKILLS IN DEALING WITH PROBLEMS, MAINLY OF COMPUTER SCIENCE, INVOLVING RANDOMNESS. ABILITY TO OUTLINE A RANDOM PHENOMENON, TO SET UP A PROBLEM AND TO SOLVE IT USING APPROPRIATE TOOLS OF PROBABILITY AND MATHEMATICAL STATISTICS, WITH PARTICULAR REFERENCE TO DISCRETE PROBABILITY AND COMBINATORICS, RANDOM VARIABLES, LIMIT THEOREMS AND THEIR APPLICATIONS TO STATISTICS. 3. MAKING JUDGEMENTS CRITICAL THINKING SKILLS. ABILITY TO IDENTIFY THE MOST APPROPRIATE METHODS TO ANALYZE AND INTERPRET PROBLEMS. 4. COMMUNICATION SKILLS ABILITY TO DISCUSS TOPICS INVOLVING PROBABILITY AND STATISTICS. 5. LEARNING SKILLS ABILITY TO ACQUIRE AND MANAGE NEW INFORMATION RELATED TO MODELS IN THE PRESENCE OF RANDOMNESS.

1. KNOWLEDGE AND UNDERSTANDING

THOROUGH UNDERSTANDING OF THE BASIC TOPICS OF PROBABILITY AND MATHEMATICAL STATISTICS. ABILITY TO IDENTIFY A PROBABILISTIC MODEL AND TO UNDERSTAND ITS MAIN FEATURES.

2. APPLYING KNOWLEDGE AND UNDERSTANDING

INDUCTIVE AND DEDUCTIVE REASONING SKILLS IN DEALING WITH PROBLEMS, MAINLY OF COMPUTER SCIENCE, INVOLVING RANDOMNESS. ABILITY TO OUTLINE A RANDOM PHENOMENON, TO SET UP A PROBLEM AND TO SOLVE IT USING APPROPRIATE TOOLS OF PROBABILITY AND MATHEMATICAL STATISTICS, WITH PARTICULAR REFERENCE TO DISCRETE PROBABILITY AND COMBINATORICS, RANDOM VARIABLES, LIMIT THEOREMS AND THEIR APPLICATIONS TO STATISTICS.

3. MAKING JUDGEMENTS

CRITICAL THINKING SKILLS. ABILITY TO IDENTIFY THE MOST APPROPRIATE METHODS TO ANALYZE AND INTERPRET PROBLEMS.

4. COMMUNICATION SKILLS

ABILITY TO DISCUSS TOPICS INVOLVING PROBABILITY AND STATISTICS.

5. LEARNING SKILLS

ABILITY TO ACQUIRE AND MANAGE NEW INFORMATION RELATED TO MODELS IN THE PRESENCE OF RANDOMNESS.

	Prerequisites
	THE STUDENT MUST HAVE ACQUIRED THE ABILITY TO DEVELOP LOGICAL-MATHEMATICAL REASONING, BASED ON NOTIONS OF MATHEMATICAL ANALYSIS, DISCRETE MATHEMATICS AND MATHEMATICAL LOGIC.

	Contents
	SAMPLE SPACE. PROBABILITY. PROBABILITY SPACE. CONDITIONAL PROBABILITY. INDEPENDENCE. RANDOM VARIABLES. DISTRIBUTION FUNCTION. MEAN, STANDARD DEVIATION, VARIANCE. DISCRETE AND CONTINUOUS RANDOM VARIABLES. POISSON PROCESS. BIDIMENSIONAL RANDOM VARIABLES. INDEPENDENCE. COVARIANCE AND CORRELATION. MOMENTS. MOMENT GENERATING FUNCTION. LINEAR COMBINATIONS OF RANDOM VARIABLES. CHEBYSHEV INEQUALITY. CONVERGENCE OF RANDOM VARIABLES. LAW OF LARGE NUMBERS. BERNOULLI THEOREM. CENTRAL-LIMIT THEOREM. APPLICATIONS. SAMPLING. STATISTICAL INFERENCE. ESTIMATION. DISTRIBUTION OF SAMPLE MEAN. FREQUENCY TABLES. DIAGRAMS. HISTOGRAMS. SAMPLE PERCENTILES. BIDIMENSIONAL DATA.

Contents

SAMPLE SPACE. PROBABILITY. PROBABILITY SPACE. CONDITIONAL PROBABILITY. INDEPENDENCE. RANDOM VARIABLES. DISTRIBUTION FUNCTION. MEAN, STANDARD DEVIATION, VARIANCE. DISCRETE AND CONTINUOUS RANDOM VARIABLES. POISSON PROCESS. BIDIMENSIONAL RANDOM VARIABLES. INDEPENDENCE. COVARIANCE AND CORRELATION. MOMENTS. MOMENT GENERATING FUNCTION. LINEAR COMBINATIONS OF RANDOM VARIABLES. CHEBYSHEV INEQUALITY. CONVERGENCE OF RANDOM VARIABLES. LAW OF LARGE NUMBERS. BERNOULLI THEOREM. CENTRAL-LIMIT THEOREM. APPLICATIONS. SAMPLING. STATISTICAL INFERENCE. ESTIMATION. DISTRIBUTION OF SAMPLE MEAN. FREQUENCY TABLES. DIAGRAMS. HISTOGRAMS. SAMPLE PERCENTILES. BIDIMENSIONAL DATA.

	Teaching Methods
	LECTURES AND CLASSROOM EXERCISES.

	Verification of learning
	CLASSROOM TEST INCLUDING THE RESOLUTION OF EXERCISES, AND A FINAL ORAL EXAMINATION WITH VERIFICATION OF KNOWLEDGE OF THE THEORETICAL ASPECTS OF THE DISCIPLINE. THE FINAL GRADE IS DETERMINED BY THE OVERALL ASSESSMENT OF THE 2 TESTS TAKEN BY THE STUDENT.

	Texts
	- ROSS S. (2010) A FIRST COURSE IN PROBABILITY. 8TH EDITION. PEARSON. - FREUND J.E., WALPOLE R.E. (1992) MATHEMATICAL STATISTICS. FIFTH EDITION. PRENTICE HALL.