What is the Example of a non-ergodic Random process (Stochastics)

Suppose that we have two coins: one coin is fair and the other has two heads. We choose (at random) one of the coins, and then perform a sequence of independent tosses of our selected coin. Let X[n] denote the outcome of the nth toss, with 1 for heads and 0 for tails. Then the ensemble average is ½  (½ +  1) = ¾; yet the long-term average is ½ for the fair coin and 1 for the two-headed coin. Hence, this random process is not ergodic in mean.