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Part B Probability Questions for Common Qualifying Examination, Spring 2007
1.
A fair coin is independently flipped
n
times,
k
times by Mary and
nk
times by
Bill.
Find the probability that Mary and Bill flip the same number of heads.
2.
Let
X
be a random variable that takes on values between 0 and
c
.
That is,
1
}
0
{
=
±
±
c
X
P
. Show that
4
)
var(
2
c
X
±
.
3.
If the density of
X
equals
Ce
2x
,
if
x>0, and 0
,
if
x<0.
Find
P{X>2}.
4.
The random variable
X
is the length of time from the start of a course of
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Unformatted text preview: medication until the remission of illness symptoms recorded in weeks. There are two types of patients: fast responders (who are 90% of patients) and slow responders. Given that a patient is a fast responder, the distribution of X is exponential with mean 2 weeks. Given that a patient is a slow responder, the distribution of X is exponential with mean 50 weeks. Find the (unconditional) mean and variance of X ....
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This note was uploaded on 01/31/2011 for the course AMS 507 taught by Professor Feinberg,e during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 Feinberg,E

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