## Quick Reference

A theorem published in 1941 that concerns the distribution of the mean, *X̄*, of *n* independent identically distributed random variables, *X*_{1}, *X*_{2},…, *X** _{n}*. The theorem requires that the expected values of

*X*

*,*

_{j}*X*

_{j}^{2}, and |

*X*

*|*

_{j}^{3}are finite and equal to 0,

*σ*

^{2}, and

*τ*, respectively. Denoting the distribution function of the standard normal distribution by Φ, the theorem states that there is a value

*c*for which , for all

*a*. The value of

*c*is known to be less than 0.766.

*Subjects:*
Probability and Statistics.