exercise:3035c98db6: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> (from Hamming<ref group="Notes" >R. W. Hamming, ''The Art of Probability for Scientists and Engineers'' (Redwood City: Addison-Wesley, 1991), p. 192.</ref>) Suppose you are standing on the bank of a straight river. <ul><li> Choose, at rando...") |
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(from Hamming<ref group="Notes" >R. W. Hamming, ''The Art of Probability for Scientists and Engineers'' (Redwood City: Addison-Wesley, 1991), p. 192.</ref>) | |||
of Probability for Scientists and Engineers'' (Redwood City: Addison-Wesley, 1991), p. 192.</ref>) | |||
Suppose you are standing on the bank of a straight river. | Suppose you are standing on the bank of a straight river. | ||
<ul><li> Choose, at random, a direction which will keep you on dry land, and walk 1 km | <ul style="list-style-type:lower-alpha"><li> 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 | in that direction. Let <math>P</math> denote your position. What is the expected distance from | ||
<math>P</math> to the river? | <math>P</math> to the river? | ||
Latest revision as of 22:53, 14 June 2024
(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