This preview shows pages 1–3. Sign up to view the full content.
Final Examination
Ramesh Johari
March 15, 2010
Instructions
1. Take alternate seating.
2. Answer all questions in the blue examination books. Answers given on any other paper will
not be counted.
3. The examination begins at 8:30 am, and ends at 11:30 am.
4. No laptop computers or networked devices are allowed, but you may use any other non
human aids you wish.
5. Show your work! Partial credit will be given for correct reasoning.
Honor Code
In taking this examination, I acknowledge and accept the Stanford University Honor Code.
NAME
(signed)
NAME
(printed)
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
1. If
X
is a geometric random variable with parameter
p
, then the pmf of
X
is:
P
(
X
=
k
) = (1
−
p
)
k
−
1
p, k
≥
1
.
2. If
X
is a binomial random variable with parameters
p
and
n
, then the pmf of
X
is:
P
(
X
=
k
) =
p
n
k
P
p
k
(1
−
p
)
n
−
k
=
n
!
k
!(
n
−
k
)!
p
k
(1
−
p
)
n
−
k
,
0
≤
k
≤
n.
3. If
T
is an exponentially distributed random variable with mean
1
/λ
, then the density of
T
is
given by
f
T
, where:
f
T
(
t
) =
λe
−
λt
,
t
≥
0
.
4. If
S
is a random variable with a gamma distribution of parameters
n
and
λ
, where
n
is a
positive integer, then the density of
S
is given by
f
S
, where:
f
S
(
s
) =
λe
−
λs
(
λs
)
n
−
1
(
n
−
1)!
,
s
This is the end of the preview. Sign up
to
access the rest of the document.
 Winter '11
 Ramesh

Click to edit the document details