Course title Fundamentals of Measurement in Physics and  Statistical Analysys
Code F107
Status Undergraduate (obligatory)
Level Basic
Year 2. Semester 3.
ECTS 4 ECTS credits
Lecturer Zvonko Glumac, Assistant Professor; Matko Mužević, Assistant
Course objective To introduce the student to basic concepts of statistics and probability. To clarify the concept of random variables and probability distribution and introduce  them as a mathematical model for actual physical problems.
Prerequisites None
Learning outcomes: After successfully completed course, students will be able to:

  1. use permutations, combinations and variations;
  2. understand the basic concepts of probability;
  3. describe the properties of binomial, Poisson, Gaussian and other distributions;
  4. use the generating function of binomial, Poisson, Gaussian and other distributions;
  5. use calculus of correlations in the statistical analysis;
  6. use Markov chains and methods of finding the equilibrium probability distributions.
Correlation of learning outcomes, teaching methods and evaluation

Teaching activity ECTS Learning outcome Students activity Methods of evaluation Points
min max
Class attendance 0 Class attendance Evidence list 0 0
Knowledge test (preliminary exam) 2 1-6 Preparation for written exam Written preliminary exam  0 50
Final exam 2 1-6 Repetition of teaching materials Oral exam (and written exam) 0 50
Total 4 1-6 0 100
Consultations Friday, 12.00 – 14.00
Gained competencies Students are prepared for scientific research, data processing and analysis of the results.
Content (Course curriculum)
  1. Introduction; permutations with and without repetition; combinations with and without repetition; variations with and without repetition; binomial theorem; definition of the basic concepts of probability; addition of probability; multiplication of probability; conditional probability; addition and multiplication theorem; Bayes’ theorem; mathematical expectation; Bernoulli probability events; Gaussian distribution; Gaussian integrals; average value; variance; Chebyshev’s theorem; law of large numbers (Bernoulli’s theorem); geometric probability; discrete and continuous probability; theorems of random variables; transformation of variables; method of least squares; error function; law of propagation of errors; the standard deviation of the mean; equalization indirect observations; basic concepts of statistics; moments of the distribution; distributions: Binomial, Poisson, hyper-geometric, Gaussian; gamma distribution; definition of generating functions; generating function of binomial, Poisson and Gaussian distribution; the addition theorem for the Gaussian distribution; generating function of gamma distribution; characteristic functions; inversion theorem; cumulative functions; central limit theorem; correlations; linear correlation; regression curve; regression lines; correlation coefficient; nonlinear correlation; index of correlation; ratio of correlation; random walk in one dimension; Markov chains; Poisson process.
Recommended reading
  1. Vjerojatnost i statistika, uvod – Z. Glumac,
  2. http://gama.fizika.unios.hr/~zglumac/uvs.pdf;
  3. Vjerojatnost i statistika, V. Vranić;
Additional reading
  1. Statistička teorija i primjena, I. Pavlić;
  2. Introduction to Probability, C. M. Grinstead and J. M. Snell.
Instructional methods Lectures (30 hours) and auditory exercises (15 hours).
Exam formats
  1. Three preliminary exams (90 min.) during the semester (50% weighting) and oral exam (50% weighting).
  2. Or, one 2-hour written examination (50% weighting) and oral exam (50% weighting).
Language Croatian or English (optional)
Quality control and successfulness follow up Student survey.
Permanent contact with students.
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