Stable distributions | Power laws | Continuous distributions | Location-scale family probability distributions | Probability distributions with non-finite variance
The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution is the distribution of the x-intercept of a ray issuing from with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero. The Cauchy distribution is often used in statistics as the canonical example of a "pathological" distribution since both its expected value and its variance are undefined (but see below). The Cauchy distribution does not have finite moments of order greater than or equal to one; only fractional absolute moments exist. The Cauchy distribution has no moment generating function. In mathematics, it is closely related to the Poisson kernel, which is the fundamental solution for the Laplace equation in the upper half-plane. It is one of the few distributions that is stable and has a probability density function that can be expressed analytically, the others being the normal distribution and the Lévy distribution. (Wikipedia).
Cauchy Sequence In this video, I define one of the most important concepts in analysis: Cauchy sequences. Those are sequences which "crowd" together, without necessarily going to a limit. Later, we'll see what implications they have in analysis. Check out my Sequences Playlist: https://w
From playlist Sequences
Intro to Cauchy Sequences and Cauchy Criterion | Real Analysis
What are Cauchy sequences? We introduce the Cauchy criterion for sequences and discuss its importance. A sequence is Cauchy if and only if it converges. So Cauchy sequences are another way of characterizing convergence without involving the limit. A sequence being Cauchy roughly means that
From playlist Real Analysis
Proof that the Sequence {1/n} is a Cauchy Sequence
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that the Sequence {1/n} is a Cauchy Sequence
From playlist Cauchy Sequences
Streaming Cauchy sequences in π
The Lie Theory Reading Group discord is https://discord.gg/MNtv4mFTkJ The code in this video you can find at https://gist.github.com/Nikolaj-K/abae34bb2d1bf73fa61235b787ecb245 Like the video last week, I use the yield keyword in Python to create an infinite stream.
From playlist Analysis
I continue the look at higher-order, linear, ordinary differential equations. This time, though, they have variable coefficients and of a very special kind.
From playlist Differential Equations
If A Sequence is Cauchy in Space it's Component Sequences are Cauchy Proof
If A Sequence is Cauchy in Space it's Component Sequences are Cauchy Proof If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Cauchy Sequences
Completeness In this video, I define the notion of a complete metric space and show that the real numbers are complete. This is a nice application of Cauchy sequences and has deep consequences in topology and analysis Cauchy sequences: https://youtu.be/ltdjB0XG0lc Check out my Sequences
From playlist Sequences
Math 101 Fall 2017 103017 Introduction to Cauchy Sequences
Definition of a Cauchy sequence. Convergent sequences are Cauchy. Cauchy sequences are not necessarily convergent. Cauchy sequences are bounded. Completeness of the real numbers (statement).
From playlist Course 6: Introduction to Analysis (Fall 2017)
Uniform Continuity and Cauchy In this video, I answer a really interesting question about continuous functions: If sn is a Cauchy sequence and f is a continuous function, then is f(sn) Cauchy as well? Surprisingly this has to do with uniform continuity. Watch this video to find out why!
From playlist Limits and Continuity
Stochastic climate models with Lévy noise by Michael Hoegele (Part 2)
ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATES: Monday 23 May, 2016 - Saturday 23 Jul, 2016 VENUE: Madhava Lecture Hall, ICTS, Bangalore This program is first-of-its-kind in India with a specific focus to p
From playlist Summer Research Program on Dynamics of Complex Systems
How to Solve Cauchy Euler Differential Equations || 8 Examples
This is a full tutorial on how to solve Cauchy Euler Differential Equations. It contains 8 complete examples and covers the cases with distinct real roots, complex roots, and repeated real roots. Udemy Courses Via My Website: https://mathsorcerer.com Free Homework Help : https://mathsor
From playlist Math Tutorials
Christian Gérard - Construction of Hadamard states for Klein‐Gordon fields
We will review a new construction of Hadamard states for quantized Klein-Gordon fields on curved spacetimes, relying on pseudo differential calculus on a Cauchy surface. We also present some work in progress where Hadamard states are constructed from traces of Klein-Gordon fields on a ch
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Search games and Optimal Kakeya Sets - Yuval Peres
Yuval Peres Microsoft Research April 28, 2014 A planar set that contains a unit segment in every direction is called a Kakeya set. These sets have been studied intensively in geometric measure theory and harmonic analysis since the work of Besicovich (1919); we find a new connection to gam
From playlist Mathematics
Cauchy principal value integral example. You learn in calculus courses that an improper integral is sometimes divergent, but in this video I show you how to make it (rigorously) equal to zero! This is widely used in distribution theory and Fourier analysis Subscribe to my channel: https:
From playlist Calculus
Christian Bär: Local index theory for Lorentzian manifolds
HYBRID EVENT We prove a local version of the index theorem for Dirac-type operators on globally hyperbolic Lorentzian manifolds with Cauchy boundary. In case the Cauchy hypersurface is compact, we do not assume self-adjointness of the Dirac operator on the spacetime or of the associated el
From playlist Mathematical Physics
Integral Transforms Lecture 7: The Fourier Transform. Oxford Mathematics 2nd Year Student Lecture
This short course from Sam Howison, all 9 lectures of which we are making available (this is lecture 7), introduces two vital ideas. First, we look at distributions (or generalised functions) and in particular the mathematical representation of a 'point mass' as the Dirac delta function.
From playlist Oxford Mathematics Student Lectures - Integral Transforms
A Finite Game of Infinite Rounds #SoME2
A short video about a random variable with no expected value. Made for the Summer of Maths Exposition 2. 0:00 Let's play a game 2:33 A better-behaved example 4:49 Working through the maths 7:08 Does the game always finish? 9:34 Discussion, and another example 11:04 A challenge problem So
From playlist Summer of Math Exposition 2 videos
Background material on the Cauchy-Riemann equations (Lecture 1) by Debraj Chakrabarti
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Twitch Talks - Probability and Statistics
Presenter: Gosia Konwerska Wolfram Research developers demonstrate the new features of Version 12 of the Wolfram Language that they were responsible for creating. Previously broadcast live on June 6, 2019 at twitch.tv/wolfram. For more information, visit: https://www.wolfram.com/language/
From playlist Twitch Talks
The Normal Distribution (1 of 3: Introductory definition)
More resources available at www.misterwootube.com
From playlist The Normal Distribution