Law of Large Numbers

Weak Law Of Large Numbers[edit | edit source]

Consider a sequence of independent random variables with a common mean . Suppose that each variable has a variance less or equal the quantity .

Consider the sample mean

Then as .

PROOF

Chebychev's inequality for each random variable :

applying to sequence :
so as .

Strong Law Of Large Numbers[edit | edit source]

Consider a sequence of independent and identically distributed random variable with a common mean . Then .

 PreviousNext