“Weak Law of Large Numbers”的概念、定义、习题解题方法及翻译-数学辞典

单词

Weak Law of Large Numbers

释义

Weak Law of Large Numbers

Also known as Bernoulli's Theorem. Let , ..., be a sequence of independent and identically distributedrandom variables, each having a Mean and Standard Deviation . Define a new variable

(1)

Then, as

, the sample mean

equals the population Mean

of each variable.

(2)



			(3)

Therefore, by the Chebyshev Inequality, for all

(4)

, it then follows that

(5)

for

arbitrarily small; i.e., as

, the sample Mean is the same as the population Mean.

Stated another way, if an event occurs times in Trials and if is the probability of successin a single Trial, then the probability that for an arbitrary Positive quantityapproaches 1 as .

See also Law of Truly Large Numbers, Strong Law of Large Numbers

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。