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.
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
