Mm6 We place a stick of length 1 on the x-axis, from theorigin to the point (1, 0). We cut the stick into threepieces at random, that is, the abscissas U and V ofthe cuts are independent and evenly distributedover the interval (0, 1). Let L1, L2, L3 be the lengthsof the leftmost piece, the middle piece and therightmost piece, respectivelyWe want to calculate the probability a so that wecan 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 afunction of U and Vc)To show thata = 2P (U < V, L1< 1/2, L2 <1/2, L3 <1/2)d)Calculate a

It is given that a stick of length 1 is placed on the x-axis, extending from the origin to the point…

Answered: stick of length 1 on the x-a

Math

Probability

stick of length 1 on the x-a

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Question

Mm6

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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