BBy Bot
Jun 09'24

Exercise

(from Hamming[Notes 1]) Suppose you are standing on the bank of a straight river.

  • Choose, at random, a direction which will keep you on dry land, and walk 1 km in that direction. Let [math]P[/math] denote your position. What is the expected distance from [math]P[/math] to the river?
  • Now suppose you proceed as in part (a), but when you get to [math]P[/math], you pick a random direction (from among all directions) and walk 1 km. What is the probability that you will reach the river before the second walk is completed?

Notes

  1. R. W. Hamming, The Art of Probability for Scientists and Engineers (Redwood City: Addison-Wesley, 1991), p. 192.