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Statistics / August 20, 2021

Statistics – Weak Law of Large Numbers

The weak law of large numbers is a result in probability theory also known as Bernoulli’s theorem. Let P be a sequence of independent and identically distributed random variables, each having a mean and standard deviation.ContentsFormulaExample Formula 0=limn→∞P{|X−μ|>1n} =P{limn→∞{|X−μ|>1n}} =P{X≠μ}0=limn→∞P{|X−μ|>1n} =P{limn→∞{|X−μ|>1n}} =P{X≠μ} Where − ·        nn = Number of samples ·        XX = Sample value ·        μμ = Sample mean Example Problem Statement: A six […]

By · August 20, 2021 · 1 min read

The weak law of large numbers is a result in probability theory also known as Bernoulli’s theorem. Let P be a sequence of independent and identically distributed random variables, each having a mean and standard deviation.

Contents

Formula

0=limn→∞P{|X−μ|>1n} =P{limn→∞{|X−μ|>1n}} =P{X≠μ}0=limn→∞P{|X−μ|>1n} =P{limn→∞{|X−μ|>1n}} =P{X≠μ}

Where −

·        nn = Number of samples

·        XX = Sample value

·        μμ = Sample mean

Example

Problem Statement:

A six sided die is rolled large number of times. Figure the sample mean of their values.

Solution:

Sample Mean Calculation

Sample Mean=1+2+3+4+5+66 =216,=3.5