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IE 523 Probabilistic Analysis
Homework # 5
Due: Monday, December 28, 08:40. To be submitted at the beginning of the Monday class.
Question 1:
Dave fails quizzes with probability 1/4, independently of other quizzes.
a.
What is the probability that Dave fails exactly two of the next six quizzes?
b.
What is the expected number of quizzes that Dave will pass before he has failed three times?
c.
What is the probability that the second and third time Dave fails a quiz will occur when he takes
his eight and ninth quizzes, respectively?
d.
What is the probability that Dave fails two quizzes in a row before he passes two quizzes in a
row?
Question 2:
A computer system carries out tasks submitted by two users. Time is divided into slots. A
slot can be idle, with probability
1/6
I
p
=
, and busy with probability
5/6
B
p
=
. During a busy slot,
there is probability
1
2/5
B
p
=
(respectively,
2
3/5
B
p
=
) that a
task from user 1 (respectively, 2) is
executed. We assume that events related to different slots are independent.
a.
Find the probability that a task from user 1 is executed for the first time during the 4
th
slot.
b.
Given that exactly 5 out of the first 10 slots were idle, find the probability that 6
th
idle slot is 12.
c.
Find the expected number of slots up to and including the 5
th
task from user 1.
d.
Find the expected number of busy slots up to and including the 5
th
task from user 1.
e.
Find the PMF, mean, and variance of the number of tasks from user 2 until the time of the 5
th
task from user 1.
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This note was uploaded on 04/15/2010 for the course INDUSTRIAL ie513 taught by Professor Zeynephuygur during the Spring '10 term at Bilkent University.
 Spring '10
 zeynephuygur

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