B015862 - PHYSICS LABORATORY III

Italian

Basic concepts of Probability. Statistics. Statistical tests. Estimators. Principle of Least Squares and Maximum Likelihood. Coverage. Statistical and systematic errors.

Electrical noise. Semiconductor diode.

Muons from cosmic rays. Decay and mean life. Liquid Scintillator Detector. Trigger system. Time measurements in nuclear physics.
Fit of time spectra for mean life estimation.

CO98:
G.Cowan - Statistical Data Analysis -- Clarendon Press (1998)
Teachers' handouts.

Knowledge acquired:
Concepts of Theory of Probability and Statistics, with applications to data analysis in the field of modern experimental Physics

Basic concepts on electrical noise and semiconductor diodes.

Basic concepts about muon and muon decay. Muon production by cosmic rays. Mean lifetime. Liquid (organic) scintillator detectors and photo multipliers tubes. Transmission lines. Some knowledge of dedicated electronics for nuclear physics measurements. Delayed coincidences method for mean lifetime estimation. Calibration of a system for time measurements in nuclear physics. Fit of particle lifetime distribution for mean life estimation.

Competence acquired:
the student is expected to become familiar with statistical analysis of experimental data, relevant to Physics and other basic sciences.


Skills acquired (at the end of the course):
the student should be able to interpret and analyse data, using fitting techniques and advanced error a
analysis.

The student should be able to derive the electric noise in a network.

Courses required: Physics laboratory II
Courses recommended: all the courses of the first and second year

CFU: 6

Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 140

Contact hours for: Lectures (hours): 40

Contact hours for: hands-on/laboratory (hours): 12

There will be an initial part of theoretical lessons for the presentation of the subjects reported in the program of the course. After that, students will have to realize experiments in the laboratory organizing, typically, in groups of three.

There is the compulsory attendance, accomplished with the presence in the laboratory during the shifts assigned.

Office hours:
Prof. Ciulli
On appointment by e-mail.

Moodle Website

Written group report on the laboratory experience and oral examination. The 5-8 page report, including figures, must be handed in at least one week before taking the oral exam. The oral exam lasts 45-50 minutes and is divided into three parts: in the first part (about 25 minutes) questions will be asked on statistics; in the second part (about 10 minutes) questions will be asked about the laboratory experience and the written report; in the third part (about 10 minutes) a question will be asked about electrical noise or about the semiconductor diode. The student must demonstrate that she/he has understood the general concepts and that she/he is able to derive the results presented in the lectures.

Probability and statistics: Basic concepts of the Theory of Probability. Komogorov's axioms. Mutually exclusive events. Conditional probability. Bayes Theorem. Independence of events. Cumulative distribution function. Probability density function (pdf). Mean value and variance. Expectation value of a random variable. Moments and central moments. Reduced (or standardized) random variables. Distribution of n random variables. Joint probability density. Marginal and conditional probability density. Independence of random variables. Covariance, correlation coefficient and covariance matrix. Transformation of 1 and n- dimension random variables. Linear transformation of random variables. Law of error propagation, i.e. law of covariance matrix transformation. Characteristic function. Characteristic function of two independent random variables. Characteristic function of a gaussian. Moments of the gaussian. Distribution of discrete random variables: binomial, multinomial, poissonian. The normal (gaussian) distribution as the limit of binomial and poissonian distribution. The Central Limit Theorem. Laplace theory of measurement errors. Distribution of continous variables: gaussian, lognormal, exponential, uniform, Cauchy's, chi-square distributions. Multivariate distribution. Multivariate distribution. Covariance ellipse. Monte Carlo techniques. Transformation and acceptance-rejection methods. Box-Mueller method. Basic Statistics. Statistical tests. P-value. Pearson's Chi-square test. Random sampling. Unbiased, biased, consistent and non-consistent estimators. The arithmetic mean as an unbiased estimator of the mean value. Weak law of large numbers. Estimators of the variance and the empiric variance. Counting statistics and relevant errors. Basic concepts of the Maximum Likelihood (ML). Criterion for determining the parameters (estimation of parameters) of a distribution, starting from a random sample of data. Principle of Least Squares (LS) and its close relationship with the ML method. LS and direct estimation of parameters (weighted mean). LS for indirect determination of parameters, for the linear and non-linear case. Errors of the parameters for the LS case. Confidence interval for the parameters. Confidence interval for a measurement and the concept of Coverage. Poissonian distribution: example of the determination of the lower limit for the lifetime a particle supposed to be unstable. Confidence interval with ML and LS methods. Confidence intervals in n-dimensions.
Electric noise: Semiconductor diode. Linear networks. Casual sequences. Noise in the frequency domain. Noise spectral density. Noise sources. Noise in a semiconductor diode.
Laboratory: Mean lifetime. Delayed coincidences method. Muons. Muon decay. Muon production by cosmic rays. Scintillation detector (liquid organic scintillator). Photo multiplier tube. A system for muon mean life measurement (trigger system, time calibrator, energy measurements). Transmission lines. Coaxial cables. Acquisition system and analysis program. Fit of spectra for mean life estimation.