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UCSD ECE153
Handout #20
Prof. YoungHan Kim
Tuesday, May 3, 2011
Midterm Examination (Spring 2008)
(Total: 80 points)
1.
First available teller (20 points).
Consider a bank with two tellers. The service times for
the tellers are independent exponentially distributed random variables
X
1
∼
Exp(
λ
1
)
and
X
2
∼
Exp(
λ
2
), respectively. You arrive at the bank and Fnd that both tellers are
busy but that nobody else is waiting to be served. You are served by the Frst available
teller once he/she becomes free. Let the random variable
Y
denote your waiting time.
±ind the pdf of
Y
.
Note: The pdf of an Exp(
λ
) random variable
X
is
f
X
(
x
) =
b
λe

λx
,
x
≥
0
,
0
,
otherwise.
2.
Sum of packet arrivals (40 points).
Consider a network router with two types of
incoming packets, wireline and wireless. Let the random variable
N
1
(
t
) denote the
number of
wireline
packets arriving during time (0
, t
] and let the random variable
N
2
(
t
) denote the number of
wireless
packets arriving during time (0
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 Spring '11
 Kim

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