Wikia

Math Wiki

Central Limit Theorem

Talk0
666pages on
this wiki

The Central Limit Theorem identifies the distribution of the sample mean and is arguably the most important theorem in probability theory.

Let X be a random variable, and let X_1, X_2, \ldots , X_n be a random sample for X, such that each X_i has a distribution identical to that of X itself. Let \overline{X} be the sample mean; in other words, let \overline{X} be equal to \frac{\sum X_i}{n}. Because each X_i is a random variable, \overline{X} is also a random variable. The Central Limit Theorem observes several important facts about the distribution of \overline{X}:

  1. The distribution of \overline{X} is approximately normal, even when the underlying distribution X is not.
  2. The expected value of the \overline{X} is equal to the expected value of X.
  3. As the sample size n increases, the variance of \overline{X} approaches zero.

See AlsoEdit

Around Wikia's network

Random Wiki