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Weak Law of Large Numbers
  • 时间:2024-11-03

Statistics - Weak Law of Large Numbers


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

Formula

$${ 0 = pm_{n o infty} P {lvert X - mu vert gt frac{1}{n} } \[7pt] = P { pm_{n o infty} { lvert X - mu vert gt frac{1}{n} } } \[7pt] = P { X e mu } }$$

Where −

    ${n}$ = Number of samples

    ${X}$ = Sample value

    ${mu}$ = 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 = frac{1+2+3+4+5+6}{6} \[7pt] = frac{21}{6}, \[7pt] , = 3.5 }$ Advertisements