# Lecture 1.1

Simulation is a way of thinking. Just as every story has actors, plots, and contexts, so does simulation. In a story, we want to know how the actors interact, under what context, and what is the outcome of their play. In simulation, random variables are our heroes, and we seek to understand how and why their interplay leads to certain outcomes.

For each simulation, we must first specify the relevant random variables. Like actors, they each have names and behaviors (personalities, characters). For example, Bernoulli, Binomial, and Normal are the names of typical random variables. Their behaviors are uniquely defined by their distribution functions—probability distribution function (PDF) $f$, or cumulative distribution function (CDF) $F$. Depending on the problem, either one can be pleasant to work with. Their relation is $F(x) = \int_{-\infty}^x f(t) dt.$

Second, we care about the context of the simulation. This is done by specifying the economic and other environmental parameters. For example, the time horizon, the production cost, and the market price. Along with the parameters of random variables, they constitute the INPUT of the simulation.

Third, we need to figure out the logic—the plot—of the simulation. That is, how the random variables interact in each context. This is the most important but least teachable part of the simulation, because the logic depends on the problem specifics, and there is no universal rule for all problems. We must analyze each on its own merit.