Paul Lévy proved a “generalized” version of this statement, which relies on the concept of alpha-stability. A version of this statement that requires the existence of moments of order 2 + delta (“two plus delta”), where delta is usually set to one, was introduced by Lyapunov. After flipping a coin 3,600 times, Abraham de Moivre proved a special case of this statement when measuring the number of “successes” in a series of independent Bernoulli trials. Textbooks often repeat the myth that this theorem provides a good approximation when N is above 30. This theorem underpins statistical inference, not the similar law of large numbers. For 10 points, name this theorem which states that the rescaled sample mean of iid (“i i d”) random variables converges to a normal distribution. ■END■
ANSWER: central limit theorem [or CLT; accept generalized central limit theorem or generalized CLT or Lyapunov central limit theorem or Lyapunov CLT]
<Other Science>
= Average correct buzz position