Notebooks related to calculations involving probability and statistics
17-4 Dice Probabilities 02-26-16
A collection of probability problems involving dice are solved. Problems range from basic probability calculations to classics like Chevalier de Mere’s problem, Pepys “sixes problem” posed to Newton, craps, etc. Emphasis is placed on compact solutions making use of Mathematica capabilities added in version 8 (2010) and afterward. Results are often checked by simulation. Over time, I intend to add more problems to this collection.
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17-36 Discrete Random Walks 07-03-16
I work through the derivation of some basic results related to discrete random walks. This work was inspired by an interesting recent paper Safe Leads and Lead Changes in Competitive Sports, Clauset, Kogan and Redner, which notes that the arcsine distribution for random walk crossings is found to occur in surprising situations, such as lead changes in NBA basketball games!
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17-37 ArcSine laws Numerical 07-05-16
numerically examine the three arcsine laws – fraction of lead time, last return time, time of maximum. Calculations are performed for Brownian motions and asymmetric Bernoulli trials. The work is related to that in notebook Discrete Random Walks 07-03-16.
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17-41 Poisson process problems 07-12-17
I present a number of calculations and problem solutions featuring Poisson Processes. The basic Poisson process is visualized and derived three different ways. Twenty three different problems involving Poisson processes are solved. Most solutions make use of Mathematica Probability capabilities with analytic solutions often cross-checked against simulation.
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