# An Interesting Question, from Victor Niederhoffer

December 30, 2015 |

An interesting question occurs when you draw two random z's from a normal distribution. What is the distribution of the difference between the two numbers? I don't believe it's the distribution of the difference between z1-z2 derived from difference between means. It's a question that comes up when you look at say a regularity or lack thereof as of 3 am, say z1, and then find another regularity at say 8 am, say z2.

Mr. Downing was a great help to Value Line and this firm, and had the ability to answer such queries in 5 to 10 seconds. And he was careful not to allow the false observations of Wang from Value Line to completely invalidate the results. He had a fairly good tennis game also. I believe Mr. Doc will answer this query within 5 minutes.

The query would seem to relate to the average absolute difference between the two numbers. The average absolute z for the first z is 0.8. The average absolute difference between the first z and the second z by simulation turns out to be 1.1 with a standard deviation of 0.85. 95% of the absolute differences will be less than 2.8 and 5% of the differences will be greater than 0.1 the algebraic differences between the two are in accord with doc's original formula of 0 mean and standard deviation of 1.4. Thus, when looking at the difference between two z's from two independent patterns, one needs a big difference of 2.8 for it to have a 5% chance of occurring by random. Thanks to doc for running the simulation.