ABSTRACT
The amount of pain involved in solving a mathematical problem is independent of
the route taken to solve it.
Proof: Follows from the general theorem, “there is no such thing as a free lunch.”
6.1 Definitions and Sample Path Properties
In Chapters 2, 3, and 4 we studied DTMCs. They arose as stochastic models of sys-
tems with countable state-space that change their state at times n = 1, 2, · · ·, and have Markov property at those times. Thus, the probabilistic nature of the future be-
havior of these systems after time n depends on the past only through their state at time n.
