# Murray Cantor

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1 commented

Great article Murray, thanks for sharing. Focal Point can really get some method out of chaotic random variables which can really help with decision making!

2 commented

By extension, my experience is that probability distributions of results are smoother than new users expect. A naive approach to a situation where cost per user is given by the triangular distribution (\$1,000, \$1,500, \$3,000) and the number of users is (20, 27, 30) is to assume that the total cost will be between \$20,000 and \$90,000. Well, the assumption is technically correct of course, but in practice the 10% value in the result distribution is much further to the right than most intuitively expect - in this case, it's at \$33,000. The 90% is ~\$64,000 - even further from the \$90,000 absolute limit. In other words, if one propagates the low and high values of the multiplication as \$20k/\$90k instead of doing the arithmetic with Monte Carlo simulation, it significantly skews the results, it just doesn't reflect reality.

3 commented

Great article that explains. Equally revealing is Jim's example in @2.

So you are making the case that where random variables are involved, Monte Carlo simulation is the approach to follow, and that Focal Point has a built in engine that does the simulation and comes up with the probability distribution, given any mathematical expression that has random variable elements in it. Would this be a fair statement?

The difficulty (at least for me) is the following: I can intuitively understand triangular distribution. Now, if there are several variables with triangular distributions, any mathematical combination of these, is not a triangular distribution; and instead has a probability distribution!

OK, I'll wait for a while for this to be become intuitive, as you guarantee :-)

4 commented

Thanks Pankaj, Jim, Sriram,

Jim surfaced an important phenomenon: As distributions are combined in some way, they generally do become smoother. Recall from the previous post on probability distributions, they can be any non-negative function with integral (area under the curve) one. That way, they can model any possible the likelihood of any set of outcomes. Triangular distributions are an especially useful kind of distribution. However, as Sriram noticed, and all should appreciate, almost any calculation with triangular distributions will not yield a triangular distribution.

However, on occasion, one uses a triangular distribution approximation to a general distribution. I will explain how that is done in my next entry.