Università Roma Tre

Classroom lectures
The scientific method: comparison between theory and experiment. Physical quantities and their measurement. The uncertainties in the measurements of physical quantities. Type A and Type B uncertainties. Measurement tools and their properties. Better estimate of the measure. Estimation of uncertainties.
Measurements, uncertainties and significant figures. Comparison between measure and expected value . Organization and presentation of data. Main properties of probability. Random events, random variables. Definition of probability: classical, frequentist, axiomatic. Total probability, conditional probability, compound probability. Bayes theorem. Statistical population. Sampling. Law of large numbers. Discrete and continuous random variables. Probability distributions. Expected value and variance. Bernoulli distribution. Poisson distribution. Gauss distribution. Probabilistic meaning of the standard deviation. Probability of obtaining a result in a measurement operation. The central limit theorem. Presentation of the result of a measure and confidence intervals. Hypothesis verification. Weighted average. Correlation between physical quantities and verification of the existence of a functional dependence: least squares method. Hypothesis test: Z test, T-Student test, Fisher test, Chi-square test.

Experiments:
Measurements of Lengths. Verification of Boyle-Mariotte law. Experiment for the determination of the spring constant. The pendulum. Measurement of gravitational acceleration with a reversible pendulum. Inclined plane. Verification of the central limit theorem (dice roll - repeated measurements). Verification of the law of radioactive decay (by means of simulation with dice). Verification of the probability distribution of Poisson (by means of Geiger).

For exam preparation, students,
in addition to consulting the teaching material made available to students on moodle (https://matematicafisica.el.uniroma3.it/):
they can consult the following texts:

C. Bini "Lezioni di Statistica per la Fisica Sperimentale" . Edizioni Nuova Cultura. Roma 2011.

Gaetano Cannelli, Metodologie sperimentali in Fisica, Introduzione al metodo scientifico, ed. EdiSES (ISBN: 978 88 7959 679 4)

GUM: Guide to the Expression of Uncertainty in Measurement - GM 100:2008
http://www.bipm.org/en/publications/guides/gum.html