• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
IB MATH STUDIES – NORMAL DISTRIBUTION EXAM
IB MATH STUDIES – NORMAL DISTRIBUTION EXAM

Notes in Introductory Real Analysis
Notes in Introductory Real Analysis

19(2)
19(2)

Continuous Probability Distributions
Continuous Probability Distributions

Elliptic Curves and The Congruent Number Problem
Elliptic Curves and The Congruent Number Problem

Linear independence of the digamma function and a variant of a conjecture of Rohrlich
Linear independence of the digamma function and a variant of a conjecture of Rohrlich

NUMBER THEORY
NUMBER THEORY

7 Catalan Numbers
7 Catalan Numbers

fermat`s little theorem - University of Arizona Math
fermat`s little theorem - University of Arizona Math

41(3)
41(3)

On the digital representation of integers with bounded prime factors
On the digital representation of integers with bounded prime factors

On Sample-Based Testers - Electronic Colloquium on
On Sample-Based Testers - Electronic Colloquium on

... Two notable exceptions appear in [22, 3], Kearns and Ron [22] consider sample-based testing (under the uniform distribution) for decision trees of a bounded size s over [0, 1]d (for constant d) and for a special class of neural networks with s hidden units. They design testers whose sample complexit ...
Section 4 Notes - University of Nebraska–Lincoln
Section 4 Notes - University of Nebraska–Lincoln

An Invitation to Sample Paths of Brownian Motion
An Invitation to Sample Paths of Brownian Motion

SUM OF TWO SQUARES Contents 1. Introduction 1 2. Preliminaries
SUM OF TWO SQUARES Contents 1. Introduction 1 2. Preliminaries

... If additionally c ≡ d (mod m), then we have: (1) a + c ≡ b + d (mod m); (2) ac ≡ bd (mod m). Furthermore, if ac ≡ bc (mod m) and c, m are relatively prime, then a ≡ b (mod m). We can now categorize the integers into classes based on their congruence modulo m, for some m > 1, by putting integers cong ...
Large gaps between consecutive prime numbers
Large gaps between consecutive prime numbers

Chapter 6 Powerpoint - peacock
Chapter 6 Powerpoint - peacock

31(2)
31(2)

View Full Page PDF - Advances in Physiology Education
View Full Page PDF - Advances in Physiology Education

1, N(3)
1, N(3)

Notes on Discrete Mathematics CS 202: Fall 2013 James Aspnes 2014-10-24 21:23
Notes on Discrete Mathematics CS 202: Fall 2013 James Aspnes 2014-10-24 21:23

Chapter 3 Density Curves Density Curves
Chapter 3 Density Curves Density Curves

Bluman_Elem_Stats_9e_CH06_PPTS
Bluman_Elem_Stats_9e_CH06_PPTS

Notes on Discrete Mathematics
Notes on Discrete Mathematics

A prime fractal and global quasi-self
A prime fractal and global quasi-self

< 1 ... 3 4 5 6 7 8 9 10 11 ... 222 >

Central limit theorem



In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution. That is, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to the normal distribution (commonly known as a ""bell curve"").The central limit theorem has a number of variants. In its common form, the random variables must be identically distributed. In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, given that they comply with certain conditions.In more general probability theory, a central limit theorem is any of a set of weak-convergence theorems. They all express the fact that a sum of many independent and identically distributed (i.i.d.) random variables, or alternatively, random variables with specific types of dependence, will tend to be distributed according to one of a small set of attractor distributions. When the variance of the i.i.d. variables is finite, the attractor distribution is the normal distribution. In contrast, the sum of a number of i.i.d. random variables with power law tail distributions decreasing as |x|−α−1 where 0 < α < 2 (and therefore having infinite variance) will tend to an alpha-stable distribution with stability parameter (or index of stability) of α as the number of variables grows.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report