Lecture

Elements of Statistics

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MICRO-428: Metrology

The course deals with the concept of measuring in different domains, particularly in the electrical, optical, and microscale domains. The course will end with a perspective on quantum measurements, which could trigger the ultimate revolution in metrology. ...

Description

This lecture covers the fundamental concepts of statistics, including probability theory, random variables, moments, covariance, and correlation. It delves into topics such as conditional probability, uniform and normal distributions, and exponential random variables. The instructor provides examples and explanations to help students understand the key principles of statistical analysis.

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Instructors (3)

Claudio Bruschini

Claudio Bruschini holds an MSc in high energy physics from the University of Genova and a PhD in Applied Sciences from the Vrije Universiteit Brussel (VUB). He started his career with INFN (Italy, 1993), in the WA92 CERN collaboration (particle physics), and then moved to CERN as a Fellow in the European GP-MIMD2 project, attached to the NA48 collaboration (particle physics, parallel programming, 1994-1995). He then started his close collaboration with EPFL, first in the DeTeC (Demining Technology Center) project (sensors for landmine detection/humanitarian demining, 1996-1997). After DeTeC's end, he started the first of a series of fruitful collaborations with the Vrije Universiteit Brussel (VUB) on humanitarian demining related R&D (1998). This was followed by the EUDEM survey project (The European Union in Humanitarian Demining, 1998), the EUDEM2 three year EC sponsored support measure (www.eudem.info, 2001-2004), and the DELVE support action (www.delve.vub.ac.be, 2007). In parallel he started working within the EPFL's AQUA group (Advanced Quantum Architectures, Edoardo Charbon), on topics as diverse as ultrasonic sensors for in-air application, optical 3D and high speed 2D sensing, sensor networks, or tracking/motion capture systems, in particular for the preparation of research projects. This culminated in the European MEGAFRAME (www.megaframe.eu, FP6, 2006-2010, SPAD arrays and related in-pixel time stamping electronics in deep submicron CMOS technology) and SPADnet (www.spadnet.eu, FP7, 2010-2014, networked SPAD arrays for Positron Emission Tomography) projects, coordinated by EPFL-AQUA. As from 2009 he also worked with Dario Floreano on the management of the CURVACE Curved Artificial Compound Eyes FP7 project (www.curvace.org), coordinated by EPFL-LIS. He was also active with CHUV (Lausanne University Hospital) within EndoTOFPET-US (endoscopic PET) as well as on a CTI project devoted to the development of a new hand-held standalone tool for tracer-guided medical procedures. In 2014 he had also the pleasure of joining the EPFL ICLAB of Christian Enz during its ramp-up phase, collaborating on device related topics (SNF GigaRadMOST) and biomedical R&D (NanoTera WiseSkin). Claudio is now fully with EPFL’s Advanced Quantum Architecture (AQUA). He has also been active as independent scientific consultant, under the label CBR Scientific Consulting, on the preparation of (European) R&D project proposals and the execution of individual studies, and worked in 2006 for a local start-up as operations manager and R&D advisor.... but this is another story. An unauthorized early biography is available at http://lami.epfl.ch/team/claudiob/...

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Mathematics

Probability theory: Topics in probability theory

Related concepts (32)

Independent and identically distributed random variables

In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as i.i.d., iid, or IID. IID was first defined in statistics and finds application in different fields such as data mining and signal processing. Statistics commonly deals with random samples. A random sample can be thought of as a set of objects that are chosen randomly.

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.

Log-normal distribution

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values.

Continuous uniform distribution

In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, and which are the minimum and maximum values. The interval can either be closed (i.e. ) or open (i.e. ). Therefore, the distribution is often abbreviated where stands for uniform distribution.

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