Statistical properties of the Moebius function

Ya. G. Sinai explains the statistical properties of the Möbius function. He starts that every positive integer n can be written as a product of primes. The first unexpected property of this sequence is that correlations depend on arithmetic properties of the number k. The relation of the Möbius function to square-free numbers is the indicator of the set of square-free numbers. He explains the properties with the help of several references and equations.