Find the correlation functions and covariance functions for the random processes given in Examples 10.1 and 10.2.

Examples 10.1

You have 1000 dollars to put in an account with interest rate R, compounded annually. That is, if X_n is the value of the account at year n, then

The value of R is a random variable that is determined when you put the money in the bank, but it does not not change after that. In particular, assume that R ∼ Uniform(0.04, 0.05).

Examples 10.2

Let {X(t), t ∈ [0,∞)} be defined as X(t) = A +Bt, for all t ∈ [0,∞),

where A and B are independent normal N(1, 1) random variables.

Transcribed Image Text:

Xn 1000 (1 + R)", = for n = 0, 1, 2,...