## Package Examples.Probability

Package description: `Examples.Probability`

See:
Description

 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 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.