200 0 5. Fw(w) %3D 1 Show that E[C\T = 15] = 18.75,
A First Course in Probability (10th Edition)
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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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Question
![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.
aning oleorly obowthat the dietribution futivn
(a) LApiany yoakK
Fr(t)
1- (1– Fx(t))(1 – Fy(t)) for t > 0,
where Fv E. are the distribution functions of v
roopootiveiy.
(b) Sun
0, 20). Stale the Image
0 <t< 20,
fr(t)
200
otherwise.
(c) The coffee will be ready at C = T + W minutes after 8:30am, where
the random variable W is independent of T and has distribution func-
tion
w < 0,
0 < w < 5,
125
w > 5.
1
Fw(w)
Show that
E[C\T = 15]
18.75,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0a3e0fd-5823-4238-a39b-386744c58d4c%2F5ce231d8-27e8-470a-9bab-4d1a0019de15%2Ft4g4i0o_processed.png&w=3840&q=75)
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.
aning oleorly obowthat the dietribution futivn
(a) LApiany yoakK
Fr(t)
1- (1– Fx(t))(1 – Fy(t)) for t > 0,
where Fv E. are the distribution functions of v
roopootiveiy.
(b) Sun
0, 20). Stale the Image
0 <t< 20,
fr(t)
200
otherwise.
(c) The coffee will be ready at C = T + W minutes after 8:30am, where
the random variable W is independent of T and has distribution func-
tion
w < 0,
0 < w < 5,
125
w > 5.
1
Fw(w)
Show that
E[C\T = 15]
18.75,
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