Sequences and series | Statistical randomness

Random sequence

The concept of a random sequence is essential in probability theory and statistics. The concept generally relies on the notion of a sequence of random variables and many statistical discussions begin with the words "let X1,...,Xn be independent random variables...". Yet as D. H. Lehmer stated in 1951: "A random sequence is a vague notion... in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests traditional with statisticians". Axiomatic probability theory deliberately avoids a definition of a random sequence. Traditional probability theory does not state if a specific sequence is random, but generally proceeds to discuss the properties of random variables and stochastic sequences assuming some definition of randomness. The Bourbaki school considered the statement "let us consider a random sequence" an abuse of language. (Wikipedia).

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What is the alternate in sign sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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What is the definition of an arithmetic sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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Introduction to Sequences (Discrete Math)

This video introduces sequences for a discrete math class. mathispower4u.com

From playlist Sequences (Discrete Math)

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What is a sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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What is an arithmetic sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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What is the difference between finite and infinite sequences

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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What is the definition of a geometric sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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What is the formula for the rule for the nth term of a arithmetic sequence

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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What is the recursive formula and how do we use it

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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Pseudorandomness

Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist Computer - Cryptography and Network Security

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Giray Ökten: Number sequences for simulation - lecture 1

After an overview of some approaches to define random sequences, we will discuss pseudorandom sequences and low-discrepancy sequences. Applications to numerical integration, Koksma-Hlawka inequality, and Niederreiter’s uniform point sets will be discussed. We will then present randomized q

From playlist Probability and Statistics

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Randomness and Kolmogorov Complexity

What does it mean for something to be "random"? We might have an intuitive idea for what randomness looks like, but can we be a bit more precise about our definition for what we would consider to be random? It turns out there are multiple definitions for what's random and what isn't, but a

From playlist Spanning Tree's Most Recent

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Giray Ökten: Number sequences for simulation - lecture 2

After an overview of some approaches to define random sequences, we will discuss pseudorandom sequences and low-discrepancy sequences. Applications to numerical integration, Koksma-Hlawka inequality, and Niederreiter’s uniform point sets will be discussed. We will then present randomized q

From playlist Probability and Statistics

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Robert Tichy: Metric Discrepancy Theory

CIRM HYBRID EVENT Recorded during the meeting "​ Diophantine Problems, Determinism and Randomness" the February 04, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathem

From playlist Analysis and its Applications

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Randomness Quiz Solution - Applied Cryptography

This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.

From playlist Applied Cryptography

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Terence Tao - The Erdős discrepancy problem [2017]

slides for this talk: https://drive.google.com/file/d/1rlGcmAWUFysSbNi6vMbrbhPyQewqDash/view?usp=sharing Terence Tao (UCLA) 2017-06-15 The Erdős discrepancy problem Many basic PDE of physical interest, such as the three-dimensional Navier-Stokes equations, are "supercritical" in that t

From playlist Mathematics

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Big Bird: Transformers for Longer Sequences (Paper Explained)

#ai #nlp #attention The quadratic resource requirements of the attention mechanism are the main roadblock in scaling up transformers to long sequences. This paper replaces the full quadratic attention mechanism by a combination of random attention, window attention, and global attention.

From playlist Deep Learning Architectures

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Asymptotic enumeration of graphs with given degree sequence – Nicholas Wormald – ICM2018

Combinatorics Invited Lecture 13.7 Asymptotic enumeration of graphs with given degree sequence Nicholas Wormald Abstract: We survey results on counting graphs with given degree sequence, focusing on asymptotic results, and mentioning some of the applications of these results. The main re

From playlist Combinatorics

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What are the formulas for arithmetic and geometric sequences

👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

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A glimpse of continuous combinatorics via natural quasirandomness - Leonardo Coregliano

Short Talks by Postdoctoral Members Topic: A glimpse of continuous combinatorics via natural quasirandomness Speaker: Leonardo Coregliano Affiliation: Member, School of Mathematics Date: September 23, 2021

From playlist Mathematics

Related pages

Impossibility of a gambling system | Random variable | D. H. Lehmer | Statistical randomness | History of randomness | Nicolas Bourbaki | Probability theory | Kolmogorov complexity | Martingale (probability theory) | Seven states of randomness | Alonzo Church | Sequence | Randomness | Statistics | Émile Borel | Probability axioms | Recursion | Universal Turing machine