The Central Limit Theorem A $Y _ { 1 } , \ldots , Y _ { n }$

The central limit theorem a. states conditions under which a variable involving the sum of $Y _ { 1 } , \ldots , Y _ { n }$ i.i.d. variables becomes the standard normal distribution.
b. postulates that the sample mean $\bar { Y }$ is a consistent estimator of the population mean $\mu _ { Y }$ .
c. only holds in the presence of the law of large numbers.
d. states conditions under which a variable involving the sum of $Y _ { 1 } , \ldots , Y _ { n }$ i.i.d. variables becomes the Student $t$ distribution.

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