The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty

CHAPTER 44

The Fundamental Identity of SLURP Algebra

What’s genuinely new about Probability Management is that SIPs and SLURPs allow probability distributions to be operated on just like numbers in a wide variety of applications. I call this property the FUNDAMENTAL IDENTITY OF SLURP ALGEBRA.

A Note from Your Author

Unless you like Red Words, I suggest that you jump to the next chapter, which describes how to actually apply this stuff. In deference to those who remain, I will forgo the aggravating Dracula font for the rest of this chapter.

As we have seen, the algebra of probability distributions is very different from that of numbers. But by keeping track of thousands of simulation trials at once, SLURP notation makes distributions much easier to think about. For example Jensen’s inequality, the central limit theorem, and interrelated uncertainties all work their way out in the wash once the CPO has set up a valid scenario library.

For this to work, all the distributions involved must pay homage to the central limit theorem, that is, the results must converge. But if they don’t, simulation doesn’t work in the first place.

Figure 44.1 P(X,Y) the SLURP of the joint distribution of X and Y is a matrix.

Let X and Y be random variables with joint distribution represented by the SLURP ...