Law of Large Numbers

In probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times.

Law of Large Numbers

Consider a sequence of $n$ i.i.d random variables; $X_1,X_2,\cdots ,X_n$ where $E(X_i)=\mu$ and $Var(X_i)={\sigma }^2\forall i$

Let ${\overline{X}}_n=\frac{1}{n}\sum _{i=1}^n{X}_i$, then $X_n\to \mu$ as $n\to \infty$

Heard this from Yingning Gui and David Silver, and learned in STAT206 omggg this is sooo cool, Serendipity.

If you are on a losing streak, you shouldn’t expect to win, because the Law of Large Numbers doesn’t really apply. It is Memorylessness

“I am due for a win”, this is Gambler’s Fallacy.