TY - JOUR
ID - 3997
TI - Bertrand’s Paradox Revisited: More Lessons about that Ambiguous Word, Random
JO - Journal of Industrial and Systems Engineering
JA - JISE
LA - en
SN - 1735-8272
AU - Chiu, Samuel S.
AU - Larson, Richard C.
AD - Department of Management Science and Engineering, Stanford University, Stanford, CA 94305 USA
AD - Engineering Systems Division and Department of Civil & Environmental Engineering, E40-233,
Massachusetts Institute of Technology, Cambridge, MA 02139 USA
Y1 - 2009
PY - 2009
VL - 3
IS - 1
SP - 1
EP - 26
KW - Bertrand paradox
KW - geometrical probability
KW - Randomness
KW - Mathematical Modeling
DO -
N2 - The Bertrand paradox question is: “Consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals 3 . Determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than 3 .” Bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random. Here we employ geometric and probability arguments to extend Bertrand’s analysis in two ways: (1) for his three classic examples, we derive the probability distributions of the chord lengths; and (2) we also derive the distribution of chord lengths for five new plausible interpretations of randomness. This includes connecting (and extending) two random points within the circle to form a random chord, perhaps being a most natural interpretation of random.
UR - http://www.jise.ir/article_3997.html
L1 - http://www.jise.ir/article_3997_6a52197644296c9501c5be1f63955e8a.pdf
ER -