The central limit theorem
A)states conditions under which a variable involving the sum of Y1,... ,Yn i.i.d.variables becomes the standard normal distribution.
B)postulates that the sample mean is a consistent estimator of the population mean .
C)only holds in the presence of the law of large numbers.
D)states conditions under which a variable involving the sum of Y1,... ,Yn i.i.d.variables becomes the Student t distribution.

Question

The central limit theorem
A)states conditions under which a variable involving the sum of Y1,... ,Yn i.i.d.variables becomes the standard normal distribution. 
B)postulates that the sample mean is a consistent estimator of the population mean . 
C)only holds in the presence of the law of large numbers. 
D)states conditions under which a variable involving the sum of Y1,... ,Yn i.i.d.variables becomes the Student t distribution.

Quizplus · Accepted Answer

The central limit theorem states that under certain conditions, the sum of i.i.d. variables will converge to a normal distribution. In other words, as n (the number of variables) gets larger, the distribution of the sum will become more and more normal. The theorem does not postulate anything about sample means or the law of large numbers, and it does not apply to the Student's t distribution.

The Central Limit Theorem