STA 4321
I
ntroduction to
P
robability
T
heory
Assignment 3
Assigned Friday February 12
Due Monday February 22
Show your work to receive full credit.
1. A study is to be conducted in a hospital to determine the attitudes of nurses toward
various administrative procedures. A sample of 5 nurses is to be selected from a total
of 20 nurses employed in the hospital. Eight of the 20 nurses are male. Let
X
represent
the number of male nurses in the sample of 5 nurses.
(a) Find the probability mass function (p.m.f) of
X
and plot it.
(b) Find the cumulative distribution function (c.d.f) of
X
and plot it.
(c) Find
E
(
X
) and
V
(
X
).
2.
(a) Verify that the function
f
(
x
) deﬁned by
f
(
x
) =
p
(1

p
)
x

1
x
=1,2,.
. .
and
f
(
x
) = 0 otherwise, is a p.m.f of a discrete random variable.
(b) Suppose Steve Nash’s career free throw percentage (
FT
%) is 90%. Suppose we
tell him to shoot
FT
0
s
indeﬁnately. Let
X
represent the number of FT’s until he
misses for the ﬁrst time. Assuming that
FT
0
s attempts are independent, what is
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 Spring '08
 Staff
 Probability, Probability theory, Cumulative distribution function, discrete random variable, Jorge Rom´n, Probability Theory Spring

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