30. Motor cars of unit length park randomly in a street in such a way that the centre of each car, in turn, is positioned uniformly at random in the space available to it. Let m(x) be the expected number of cars which are able to park in a street of length x. Show that m(x + 1) = = √ √ * {m(y) + m(x − y) + 1} dy. X It is possible to deduce that m(x) is about as big as x when x is large.
30. Motor cars of unit length park randomly in a street in such a way that the centre of each car, in turn, is positioned uniformly at random in the space available to it. Let m(x) be the expected number of cars which are able to park in a street of length x. Show that m(x + 1) = = √ √ * {m(y) + m(x − y) + 1} dy. X It is possible to deduce that m(x) is about as big as x when x is large.
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:30. Motor cars of unit length park randomly in a street in such a way that the centre of each car, in
turn, is positioned uniformly at random in the space available to it. Let m(x) be the expected number
of cars which are able to park in a street of length x. Show that
m(x + 1) = = √ √ * {m(y) + m(x − y) + 1} dy.
It is possible to deduce that m(x) is about as big as x when x is large.
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