Package Examples.Probability

Package description: Examples.Probability

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Class Summary
DirichletDemo A two dimensional Brownian motion is started at the origin and the path * displayed until it hits the boundary of the unit circle.
DirichletProblem We solve the Dirichlet problem on the unit disk with boundary function * h(x,y)=x*y (which is harmonic on the entire plane).
EmpiricalHistogram A data set of N=2000 standard normal random draws is generated.
ExpectationTest  
GamblersFortune Console program setting up a biased random walk X and checking the * gambler's expected winnings (losses really) and the probability of losing it * all under the following stopping rule:
GamblersFortune_1 Gambler starts with 6 dollars and bets 1 dollar on unfavorably loaded * coin (0.49/0.51) until he has 10 dollars or is wiped out.
Insurance Console program computing probability of ruin faced by an insurance * company hit with claims coming in as a compound Poisson process.
OptionalSamplingTest We set up a symmetric random walk X (a martingale) and check the Optional * Sampling Theorem (E(X_Tau)=X_0) for a hitting time Tau (the first exit time * from the interval [-20,20]).
PathBranchDemo Main method provides animated graphics to illustrate the concept of conditioning through path branching.
PathFunctionalHistogram Displays a histogram of the run time maximum of a standard Brownian motion (200,000 paths, 100 bins).
Urns Two urns are filled with 100 white respectively 200 black balls.
 

Package Examples.Probability Description

Package description: Examples.Probability

Various examples illustrating the use of classes in the packages Statistics and Processes (random variables and vectors, stochastic processes and optional times). Please proceed to the descriptions of the individual classes for details.