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ENEE 324
ASSIGNMENT 22
Due Thu 12/10
Problem 22A
Consider a Poisson arrival process
{
N
(
t
)
, t >
0
}
(where
t
is in seconds) of rate
λ
= 2 arrivals/sec.
(i) (2 pts.)
Determine
P
[
N
(4) = 8].
(ii) (3 pts.)
Determine
P
[
N
(5) = 10

N
(1) = 2].
(iii) (3 pts.)
Given that there were ten arrivals in the time interval (0
,
5], what is the conditional
probability that there were no arrivals in either (0
,
1] or (4
,
5]?
(iv) (2 pts.)
Given that there were ten arrivals in the time interval (0
,
10], what is the conditional
probability that there were no arrivals in either (0
,
2] or (8
,
10]?
(v) (3 pts.)
Given that there were ten arrivals in the time interval (0
,
5], what is the conditional
probability that there were two arrivals every second, i.e., in (0
,
1], (1
,
2], etc.?
(vi) (5 pts.)
Determine
P
[
N
(5)

N
(3) = 2

N
(4) = 8].
(vii) (2 pts.)
If
{
M
(
t
)
, t >
0
}
is a also a Poisson arrival process with rate
λ
= 3 arrivals/sec,
what is the relationship between the expected time of the second arrival in
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 Fall '05
 Ephrimedes

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