The Problem of the Random Walk

@article{PearsonThePO,
  title={The Problem of the Random Walk},
  author={Karl Pearson},
  journal={Nature},
  volume={72},
  pages={294-294}
}
CAN any of your readers refer me to a work wherein I should find a solution of the following problem, or failing the knowledge of any existing solution provide me with an original one? I should be extremely grateful for aid in the matter. 

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