Lesson 1

Informally, the law of large numbers states that to improve measurement results, one should repeat the measurement many times and then take the average of the results. This reduces variance. For example, the expected value of a die roll is \(3.5\), and the variance is \(\frac{35}{12}\). If the die is rolled a thousand times and the average is taken (i.e., considering a random variable equal to the mean of the results), the expected value remains \(3.5\), while the variance becomes \(\frac{35}{12\ 000}\).