Fields of geometry | Probability theory
Problems of the following type, and their solution techniques, were first studied in the 18th century, and the general topic became known as geometric probability. * (Buffon's needle) What is the chance that a needle dropped randomly onto a floor marked with equally spaced parallel lines will cross one of the lines? * What is the mean length of a random chord of a unit circle? (cf. Bertrand's paradox). * What is the chance that three random points in the plane form an acute (rather than obtuse) triangle? * What is the mean area of the polygonal regions formed when randomly oriented lines are spread over the plane? For mathematical development see the concise monograph by Solomon. Since the late 20th century, the topic has split into two topics with different emphases. Integral geometry sprang from the principle that the mathematically natural probability models are those that are invariant under certain transformation groups. This topic emphasises systematic development of formulas for calculating expected values associated with the geometric objects derived from random points, and can in part be viewed as a sophisticated branch of multivariate calculus. Stochastic geometry emphasises the random geometrical objects themselves. For instance: different models for random lines or for random tessellations of the plane; random sets formed by making points of a spatial Poisson process be (say) centers of discs. (Wikipedia).
Probability: We define geometric random variables, and find the mean, variance, and moment generating function of such. The key tools are the geometric power series and its derivatives.
From playlist Probability
Expectation of a geometric random variable
How to compute the expectation of a geometric random variable.
From playlist Probability Theory
Learn how to find the geometric probability from a figure
Learn how to find the geometric probability of an event. Given a geometric figure, we can find the geometric probability of an event by taken the area of the part of the geometric figure satisfying the event divided by the area of the entire geometric figure.
From playlist Find the Geometric Probability #Probability
(PP 6.7) Geometric intuition for the multivariate Gaussian (part 2)
How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.
From playlist Probability Theory
(PP 6.6) Geometric intuition for the multivariate Gaussian (part 1)
How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.
From playlist Probability Theory
Statistics: Introduction to Geometric Distribution Probabilities
This video introduces distribution probabilities. http://mathispower4u.com
From playlist Geometric Probability Distribution
Geometric Distribution - Probability, Mean, Variance, & Standard Deviation
This statistics video tutorial explains how to calculate the probability of a geometric distribution function. It also explains how to calculate the mean, variance, and standard deviation. It contains plenty of example problems with the formulas needed to solve them. My Website: https:
From playlist Statistics
Geometric Distribution: Probability, Mean, and Standard Deviation
This explains how to determine a probability, the mean, and standard deviation of a geometric distribution. http://mathispower4u.com
From playlist Geometric Probability Distribution
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
Geometric Setting & Distribution in Statistics
I introduce the Geometric Setting & Distribution in statistics and compare it to the Binomial Setting. This video includes setting up a PDF, examples of finding probabilities, and a non-example of a geometric setting. Find free review test, useful notes and more at http://www.mathplane.co
From playlist AP Statistics
This is an old video. See StatsMrR.com for access to hundreds of 1-3 minute, well-produced videos for learning Statistics. In this older video: Work with Geometric probabilities and compare and contrast with binomial
From playlist Older Statistics Videos and Other Math Videos
L06.6 Geometric PMF Memorylessness & Expectation
MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu
From playlist MIT RES.6-012 Introduction to Probability, Spring 2018
Geometric Distributions and The Birthday Paradox: Crash Course Statistics #16
Geometric probabilities, and probabilities in general, allow us to guess how long we'll have to wait for something to happen. Today, we'll discuss how they can be used to figure out how many Bertie Bott's Every Flavour Beans you could eat before getting the dreaded vomit flavored bean, and
From playlist Statistics
Live CEOing Ep 97: Geometry in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Geometry in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Proof of expected value of geometric random variable | AP Statistics | Khan Academy
Proof of expected value of geometric random variable. View more lessons or practice this subject at http://www.khanacademy.org/math/ap-statistics/random-variables-ap/geometric-random-variable/v/proof-of-expected-value-of-geometric-random-variable?utm_source=youtube&utm_medium=desc&utm_cam
From playlist Random variables | AP Statistics | Khan Academy
MIT 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010 View the complete course: http://ocw.mit.edu/6-041F10 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
#60 Geometric Deep Learning Blueprint (Special Edition)
Patreon: https://www.patreon.com/mlst Discord: https://discord.gg/ESrGqhf5CB "Symmetry, as wide or narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection." and that was a quote from Hermann Weyl, a G
From playlist Interviews
AMMI 2022 Course "Geometric Deep Learning" - Lecture 1 (Introduction) - Michael Bronstein
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 by Michael Bronstein (Oxford), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 1: Symmetry through the centuries • First neural networ
From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)
Live CEOing Ep 195: Geometry in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Geometry in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
How to determine the altitude by using the geometric mean
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN