ISYE 2027 Chapter Notes - Chapter 14: Independent And Identically Distributed Random Variables, Central Limit Theorem, Random Variable

• School: Georgia Tech
• Department: Industrial & Systems Engr
• Course: ISYE 2027
• Professor: All

Document Summary

Dklm chapter 14: the central limit theorem: 14. 1 standardizing averages, in the previous chapter we saw that the law of large numbers guarantees the convergence to of the average xbarn of n independent random variables x. , = 1,2, : the central limit theorem: let x1, x2, be any sequence of independent identically distributed random variables with finite positive variance. Let be the expected value and + the variance of each of the xi . for n 1, let zn be defined. " l is the distribution function of the n(0,1) distribution. N8 = () where : the distribution function of zn converges to the distribution function of the standard normal, one can also write zn as a standardized sum: " =