# Is the Weak Law of Large Numbers only true for Bernoulli trials?

I wonder if the Weak Law of Large Numbers is only applicable if the random variable is binomially distributed. (The random variable counts the relative frequency of an event A). So, when you describe the Law, do you have to mention as a prerequisite that you only look at Bernoulli experiments?

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As long as the $X_i$ are independent identically distributed, and their mean exists, the sample mean converges in probability to the mean. There is no need to have the $X_i$ be Bernoulli.
@Sai: I guess the Bernoulli case is the closest to the intuition. The Chebyshev Inequality argument works in exactly the same way for $X_i$ that have a variance. The result holds more generally, but for $X_i$ that don't have a variance the proof involves more advanced ideas. –  André Nicolas Jun 26 '12 at 13:59