stick of length 1 on the x-a
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:We place a stick of length 1 on the x-axis, from the
origin to the point (1, 0). We cut the stick into three
pieces at random, that is, the abscissas U and V of
the cuts are independent and evenly distributed
over the interval (0, 1). Let L1, L2, L3 be the lengths
of the leftmost piece, the middle piece and the
rightmost piece, respectively
We want to calculate the probability a so that we
can make a triangle with the three pieces 1.
a)
What is the event for which a is the probability?
b)
Express the random variables L1, L2 and L3 as a
function of U and V
c)
To show that
a = 2P (U < V, L1< 1/2, L2 <1/2, L3 <1/2)
d)
Calculate a
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