) Suppose now that X ~ U(0, 20) and Y ~ U (0, 20). State the image of T, Im T. Find the distribution function Fr(t). Hence show that the density function fr(t) is given by 0
) Suppose now that X ~ U(0, 20) and Y ~ U (0, 20). State the image of T, Im T. Find the distribution function Fr(t). Hence show that the density function fr(t) is given by 0
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:One day, Alison cycles to work, and her journey time is X minutes. On
the same day, Bob drives to work, and his journey time is Y minutes.
You may assume that X and Y are independent random variables.
Both Alison and Bob start their journey to work at 8:30am, and the first
to arrive switches on the coffee machine as soon as they arrive.
Denote by T the number of minutes after 8:30am that the coffee machine
is switched on.
(e Euplaining y Aoning olaauly ohow that ihe disubuion Tucuon
Tcotinfies
Fr(t) = 1-
(1 – Fx(t))(1 – Fy(t)) for t > 0,
apittoro ,Parethe distribution function
reopectivoly
(b) Suppose now that X
of T, Im T. Find the distribution function FrT(t). Hence show that the
density function fr(t) is given by
· U (0, 20) and Y ~
U (0, 20). State the image
0<t< 20,
otherwise.
fr(t)
10
200
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