# Process analysis example essays

Suppose that you start with $10, and you wager$1 on an unending, fair, coin toss indefinitely, or until you lose all of your money. If X n {\displaystyle X_{n}} represents the number of dollars you have after n tosses, with X 0 = 10 {\displaystyle X_{0}=10} , then the sequence { X n : n ∈ N } {\displaystyle \{X_{n}:n\in \mathbb {N} \}} is a Markov process. If I know that you have $12 now, then it would be expected that with even odds, you will either have$11 or $13 after the next toss. This guess is not improved by the added knowledge that you started with$10, then went up to $11, down to$10, up to $11, and then to$12.