statisticalrethinkin..

4.1. WHY NORMAL DISTRIBUTIONS ARE NORMAL 85position-6 -3 0 3 60 4 8 12 16step numberDensity0.0 0.2 0.44 stepsDensity0.00 0.15 0.308 stepsDensity0.00 0.10 0.2016 steps-6 -3 0 3 6-6 -3 0 3 6-6 -3 0 3 6positionpositionpositionFIGURE 4.2. Random walks on the soccer field converge to a normal distribution.e more steps are taken, the closer the match between the realempirical distribution of positions and the ideal normal distribution, superimposedin the last plot in the bottom panel.flipped, a distance between zero and one yard is taken in the indicated direction, and theprocess repeats. To simulate this, we generate for each person a list of 16 random numbersbetween −1 and 1. ese are the individual steps. en we add these steps together to getthe position aer 16 steps. en we need to replicate this procedure one-thousand times.is is the sort of task that would be harrowing in a point-and-click interface, but it is madetrivial by the command line. Here’s a single line to do the whole thing:pos