Prepared Direct Testimony of Robert McCullough on Behalf of the ...

Page 19 <strong>of</strong> 76SEATAC-400each time period. Some plants are "available" and contribute their total capacity to this sum,while others are "unavailable" and add zero.Fourth, the statistical distribution <strong>of</strong> the variable <strong>of</strong> interest is evaluated. In our application, wehave a particular interest in the probability that the total available capacity is less than someparticular proportion <strong>of</strong> the total possible capacity. As a statistical statement, we are looking forthe value <strong>of</strong> a probability distribution function at a particular availability percentage.Q. Are there other problems that clearly illustrate how this approach works in evaluatingthe likelihood <strong>of</strong> complex events?A. An analogous problem is the question <strong>of</strong> how likely it is to roll ten dice simultaneously, assign avalue <strong>of</strong> zero to a die if it comes up six and a value <strong>of</strong> one otherwise, add up the values and get atotal less than or equal to five. This problem can be solved analytically, but is easily explored byjust throwing ten dice many times and tabulating the results. The problem is more difficult tosolve analytically if the dice have different numbers <strong>of</strong> faces - e.g. a mix <strong>of</strong> normal cubical dice,octrahedral dice, tetrahedral dice - and the values assigned to each die are different functions <strong>of</strong>how the die falls, and if there are many more dice. In that case, a convincing demonstration canstill be made by actually conducting the experiment, throwing the dice many tirnes and keepingtabs on the results.Q. How would this roll-<strong>of</strong>-the-dice example relate to the study you performed?A. The capacity availability Monte Carlo study we performed involved ten thousand ''throws <strong>of</strong> thedice."Q. How likely would the real world capacity availability for these plants be if the simple