## Probability proof

LetF(x)=P{X≤x} where X is some random variable on {Ω,F,P}. For
any n₁, ..., n_{k} where k ≥0 and different n_{i} ≥0 (that is n_{i} ≠ n_{j} , if i ≠ j) we
define a function
F_{n₁,...,n_{k}}(x₁,..,x_{k}) =∏F(x_{i})

(a) Show that F defines the family of k- dimensional distributions of some
random sequence Xn.
(b) Prove that Xn and Xm are independent for n ≠ m.

(c) Find the mean and autocorrelation function of this sequence