Random walk

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Apparently, the so-called random walk problem was set out by Karl Pearson in a letter to Nature in 1905 (Ref. 1)

"A man starts from a point O and walks l yards in a straight line; he then turns through any angle whatever and walks another l yards in a second straight line. He repeats this process n times. I require the probability that after these n stretches he is at a distance between r and r + dr from his starting point, O."

References

  1. Karl Pearson "The Problem of the Random Walk", Nature 72 p. 294 (1905)
  2. Ian Stewart "Mathematics: Where drunkards hang out", Nature 413 pp. 686-687 (2001)