Functions related to probability distributions
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. In a more precise sense, the PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of this variable's PDF over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and the area under the entire curve is equal to 1. The terms "probability distribution function" and "probability function" have also sometimes been used to denote the probability density function. However, this use is not standard among probabilists and statisticians. In other sources, "probability distribution function" may be used when the probability distribution is defined as a function over general sets of values or it may refer to the cumulative distribution function, or it may be a probability mass function (PMF) rather than the density. "Density function" itself is also used for the probability mass function, leading to further confusion. In general though, the PMF is used in the context of discrete random variables (random variables that take values on a countable set), while the PDF is used in the context of continuous random variables. (Wikipedia).
(PP 3.4) Random Variables with Densities
(0:00) Probability density function (PDF). (3:20) Indicator functions. (5:00) Examples of random variables with densities: Uniform, Exponential, Beta, Normal/Gaussian. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5
From playlist Probability Theory
Example of Probability Density Function
Probability: The value of a randomly selected car is given by a random variable X whose distribution has density function f(x) =x^{-2} for x gt 1. Given that the value of a given randomly selected car is greater than 5, calculate the probability that the value is less than or equal to 1
From playlist Probability
Chp9Pr41: Probability Density Functions
A continuous random variable can be described using a function called the probability density function. This video shows us how to prove that a function is a probability density function. This is Chapter 9 Problem 41 from the MATH1231/1241 algebra notes. Presented by Dr Diana Combe from th
From playlist Mathematics 1B (Algebra)
This calculus 2 video tutorial provides a basic introduction into probability density functions. It explains how to find the probability that a continuous random variable such as x in somewhere between two values by evaluating the definite integral from a to b. The probability is equival
From playlist New Calculus Video Playlist
Probability Density Function of the Normal Distribution
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From playlist Random Variables
Probability Density Functions (3 of 7: Unknowns in the function)
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From playlist Random Variables
(PP 6.4) Density for a multivariate Gaussian - definition and intuition
The density of a (multivariate) non-degenerate Gaussian. Suggestions for how to remember the formula. Mathematical intuition for how to think about the formula.
From playlist Probability Theory
Probability Distribution Functions
We explore the idea of continuous probability density functions in a classical context, with a ball bouncing around in a box, as a preparation for the study of wavefunctions in quantum mechanics.
From playlist Quantum Mechanics Uploads
Probability Distribution Functions and Cumulative Distribution Functions
In this video we discuss the concept of probability distributions. These commonly take one of two forms, either the probability distribution function, f(x), or the cumulative distribution function, F(x). We examine both discrete and continuous versions of both functions and illustrate th
From playlist Probability
Probability Density Function With Example | Probability And Statistics Tutorial | Simplilearn
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9. Multiple Continuous Random Variables
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
Lec 7 | MIT 5.112 Principles of Chemical Science, Fall 2005
Hydrogen Atom Wave functions View the complete course: http://ocw.mit.edu/5-112F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 5.112 Principles of Chemical Science, Fall 2005
8. Continuous Random Variables
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
Lec 8 | MIT 5.112 Principles of Chemical Science, Fall 2005
P Orbitals View the complete course: http://ocw.mit.edu/5-112F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 5.112 Principles of Chemical Science, Fall 2005
Virginie Ehrlacher - Sparse approximation of the Lieb functional in DFT with moment constraints
Recorded 28 March 2023. Virginie Ehrlacher of the École Nationale des Ponts-et-Chaussées presents "Sparse approximation of the Lieb functional in DFT with moment constraints (joint work with Luca Nenna)" at IPAM's Increasing the Length, Time, and Accuracy of Materials Modeling Using Exasca
From playlist 2023 Increasing the Length, Time, and Accuracy of Materials Modeling Using Exascale Computing
Lec 7 | MIT 5.111 Principles of Chemical Science, Fall 2005
Hydrogen Atom Wavefunctions (Prof. Sylvia Ceyer) View the complete course: http://ocw.mit.edu/5-111F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 5.111 Principles of Chemical Science, Fall 2005
Introduction to Probability and Statistics 131A. Lecture 5. Expected Values
UCI Math 131A: Introduction to Probability and Statistics (Summer 2013) Lec 05. Introduction to Probability and Statistics: Expected Values View the complete course: http://ocw.uci.edu/courses/math_131a_introduction_to_probability_and_statistics.html Instructor: Michael C. Cranston, Ph.D.
From playlist Math 131A: Introduction to Probability and Statistics
Lecture 19: Generative Models I
Lecture 19 is the first of two lectures about generative models. We compare supervised and unsupervised learning, and also compare discriminative vs generative models. We discuss autoregressive generative models that explicitly model densities, including PixelRNN and PixelCNN. We discuss a
From playlist Tango
Cumulative Distribution Functions and Probability Density Functions
This statistics video tutorial provides a basic introduction into cumulative distribution functions and probability density functions. The probability density function or pdf is f(x) which describes the shape of the distribution. It can tell you if you have a uniform, exponential, or nor
From playlist Statistics
Hazard and Survival Functions - [Survival Analysis 5/8]
See all my videos at https://www.zstatistics.com/ Any donations via the Super Thanks button going to the Right To Learn Foundation: https://www.right2learnfoundation.org/about-us/ Survival analysis playlist here: https://youtube.com/playlist?list=PLTNMv857s9WUclZLm6OFUW3QcXgRa97jx 0:00
From playlist Survival Analysis