Law of large numbers : According to the law of large numbers $\lim \limits_{n \to \infty} \frac{1}{n}\sum_{i=1}^{n}X_i=E[X]$ for independent identical distributed random variables $X_1, X_2,...$ This means that the average outcome of an independently repeated random experiment converges to the expected value. For example the law of large numbers implies that the average of a large number of dice throws converges to 3.5.