A bell-shaped function or simply 'bell curve' is a mathematical function having a characteristic "bell"-shaped curve. These functions are typically continuous or smooth, asymptotically approach zero for large negative/positive x, and have a single, unimodal maximum at small x. Hence, the integral of a bell-shaped function is typically a sigmoid function. Bell shaped functions are also commonly symmetric. Many common probability distribution functions are bell curves. Some bell shaped functions, such as the Gaussian function and probability distribution of the Cauchy distribution, can be used to construct sequences of functions with decreasing variance that approach the Dirac delta distribution. Indeed, the Dirac delta can roughly be thought of as a bell curve with variance tending to zero. Some examples include: * Gaussian function, the probability density function of the normal distribution. This is the archetypal bell shaped function and is frequently encountered in nature as a consequence of the central limit theorem. * Fuzzy Logic generalized membership bell-shaped function * Hyperbolic secant. This is also the derivative of the Gudermannian function. * Witch of Agnesi, the probability density function of the Cauchy distribution. This is also a scaled version of the derivative of the arctangent function. * Bump function * Raised cosines type like the raised cosine distribution or the raised-cosine filter * Most of the window functions like the Kaiser window * The derivative of the logistic function. This is a scaled version of the derivative of the hyperbolic tangent function. * Some algebraic functions. For example (Wikipedia).
Represent a Discrete Function Using Ordered Pairs, a Table, and Function Notation
This video explains how to represent a discrete function given as points as ordered pairs, a table, and using function notation. http://mathispower4u.com
From playlist Introduction to Functions: Function Basics
Bell Labs Wave Machine: Standing Waves
Standing waves are created on the Bell Labs apparatus. The apparatus is "open" at both ends, therefore the number of nodes is equal to the number of overtones. For example, the fourth harmonic will have four nodes, the fifth harmonic will have five nodes, etc.
From playlist Bell Labs Wave Machine
Working with Functions (1 of 2: Notation & Terminology)
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From playlist Working with Functions
Describing Functions (Discrete Math)
This video covered the various ways to describe functions in a discrete math class.
From playlist Functions (Discrete Math)
In this video we cover some rational function fundamentals, including asymptotes and interecepts.
From playlist Polynomial Functions
Determine if a Function is a Polynomial Function
This video explains how to determine if a function is a polynomial function. http://mathispower4u.com
From playlist Determining the Characteristics of Polynomial Functions
Introduction to Functions (2 of 2: Visualising examples & counter-examples)
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From playlist Working with Functions (related content)
2.11117 What is a rational function Functions
http://www.freemathvideos.com presents: Learn math your way. My mission is to provide quality math education to everyone that is willing to receive it. This video is only a portion of a video course I have created as a math teacher. Please visit my website to join my mailing list, downloa
From playlist Rational Functions - Understanding
This video explains what a mathematical function is and how it defines a relationship between two sets, the domain and the range. It also introduces three important categories of function: injective, surjective and bijective.
From playlist Foundational Math
Excel Statistical Analysis 32: Bell Curve Functions: NORM.DIST, NORM.S.DIST, NORM.INV, NORM.S.INV
Download Excel File: https://excelisfun.net/files/Ch06-ESA.xlsm PDF notes file: https://excelisfun.net/files/Ch06-ESA.pdf Learn about the Normal (Bell) Probability Distribution and the Excel worksheet functions to calculate probability and x values: NORM.DIST, NORM.S.DIST, NORM.INV, NORM.
From playlist Excel Statistical Analysis for Business Class Playlist of Videos from excelisfun
Excel 2013 Statistical Analysis #39: Probabilities for Normal (Bell) Probability Distribution
Download files (which file shown at begin of video): https://people.highline.edu/mgirvin/AllClasses/210Excel2013/Ch06/Ch06.htm Topics in this video: 1. (00:11) Using Handwritten notes, discuss characteristics of the Normal (Bell) Distribution, how to calculate probabilities using Excel fun
From playlist Excel for Statistical Analysis in Business & Economics Free Course at YouTube (75 Videos)
Excel 2010 Statistics #18: Frequency Distribution Shape & Histogram Skew & Sparklines
Download Excel File: https://people.highline.edu/mgirvin/AllClasses/210Excel2010/Content/Ch02/Busn210Excel2010Chapter02.xlsm 1. Learn about the importance of the shape of the data: Frequency Distribution Shape 2. Skew in Histograms 3. New Excel 2010 Sparkline Cell Charts 4. Learn about ho
From playlist Excel 2010 Videos
Excel Statistical Analysis 14: Z-Score, Empirical Rule , Chebyshev Theorem: # of Standard Deviations
Download Excel File: https://excelisfun.net/files/Ch03-ESA.xlsm Learn about the z-score (number of standard deviations) and how to calculate it and use it in the Empirical Rule and Chebyshev's Theorem. Topics: 1. (00:00) Introduction to Z-Score 2. (01:23) Basics of Z-Score Calculations usi
From playlist Excel Statistical Analysis for Business Class Playlist of Videos from excelisfun
Excel 2010 Statistics 56: Normal (Bell) & Standard Normal Characteristics
Download Excel File: https://people.highline.edu/mgirvin/AllClasses/210Excel2010/Content/Ch06/Busn210ch06.xlsm Download pdf file: https://people.highline.edu/mgirvin/AllClasses/210Excel2010/Content/Ch06/Busn210Ch06.pdf Topics for Continuous Probability Distributions:: 1. See Dynamic Char
From playlist Excel 2010 Statistics Formulas Functions Charts PivotTables
Excel Statistics 68: Normal (Bell) & Standard Normal Characteristics
Download Excel File: https://people.highline.edu/mgirvin/AllClasses/210M/Content/ch06/Busn210ch06.xls Download pdf notes: https://people.highline.edu/mgirvin/AllClasses/210M/Content/ch06/Busn210Ch06.pdf Topics for Continuous Probability Distributions:: 1.See Dynamic Chart examples of th
From playlist Excel Statistics B. 06: Continuous Probability Distributions
Excel 2010 Statistics #31: z-Scores, Chebyshev's Theorem and Empirical Rule
Download Excel File #1: https://people.highline.edu/mgirvin/AllClasses/210Excel2010/Content/Ch03/Excel2010StatisticsCh03correct.xlsm Download Excel File #2: https://people.highline.edu/mgirvin/AllClasses/210Excel2010/Content/Ch03/Excel2010StatisticsCh03SecondFile.xlsm Download Excel File #
From playlist Excel 2010 Statistics Formulas Functions Charts PivotTables
Excel 2013 Statistical Analysis #21: SKEW Function and Asymmetry in a Distribution of Data Points
Download file: https://people.highline.edu/mgirvin/AllClasses/210Excel2013/Ch03/Excel2013StatisticsChapter03.xlsm This video covers skew in a distribution of data points and the SKEW function.
From playlist Excel for Statistical Analysis in Business & Economics Free Course at YouTube (75 Videos)
Multivariate Gaussian distributions
Properties of the multivariate Gaussian probability distribution
From playlist cs273a
Notation and Basic Signal Properties
http://AllSignalProcessing.com for free e-book on frequency relationships and more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Signals as functions, discrete- and continuous-time signals, sampling, images, periodic signals, displayi
From playlist Introduction and Background
Excel & Statistics 44: Skew & SKEW function
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From playlist Excel 2007 Statistics: Charts, Functions, Formulas