For each of the following determine whether or not the

Question

For each of the following, determine whether or not the random process is

i. Wide-sense stationary.

ii. Mean ergodic.

(a) x(n) = A where A is a random variable with probability density function f_A(α).

(b) x (n) = A cos(nw₀) where A is a Gaussian random variable with mean m A and variance σ²_A.

(c) x(n) = A cos(nw₀ + ) where is a random variable that is uniformly distributed between -n and n.

(d) x(n) = A cos(nw₀ ) + B sin(nw0) where A and Bare uncorrelated zero mean random variables with variance a 2 •

(e) A Bernoulli process with Pr{x(n) = 1} = p and Pr{x(n) = -1} = 1 - p.

(f) y(n) = x(n) - x(n - 1) where x(n) is the Bernoulli process defined in part (e).