Mathematical and Applied Statistics Lesson of the Day – The Central Limit Theorem Can Apply to the Sum
June 9, 2014 Leave a comment
The central limit theorem (CLT) is often stated in terms of the sample mean of independent and identically distributed random variables. An often unnoticed or forgotten aspect of the CLT is its applicability to the sample sum of those variables, too. Since , the sample size, is just a constant, it can be multiplied to to obtain . For a sufficiently large , this new statistic still has an approximately normal distribution, just with a new expected value and a new variance.