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. (a) Explaining your reasoning clearly, show that the distribution function Fr of T satisfies Fr(t) = 1- (1 – Fx(t))(1 – Fy(t)) for t > 0, where Fx, Fy are the distribution functions of X,Y, respectively.
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. (a) Explaining your reasoning clearly, show that the distribution function Fr of T satisfies Fr(t) = 1- (1 – Fx(t))(1 – Fy(t)) for t > 0, where Fx, Fy are the distribution functions of X,Y, respectively.
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.
(a) Explaining your reasoning clearly, show that the distribution function
Fr of T satisfies
Fr(t) =
1– (1 – Fx(t))(1– Fy(t)) for t > 0,
where Fx, Fy are the distribution functions of X,Y, respectively.
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