Stat 400 In Class Worksheet 10
T.A. Emily King
April 16, 2008
1. (Modified from book p. 202 # 27) Annie and Alvie have agreed to meet
for lunch between noon (0:00 PM) and 1:00 PM. Denote Annie’s arrival
time by
X
, Alvie’s by
Y
and suppose that
X
and
Y
are independent with
pdf’s
f
X
(
x
)
=
3
x
2
0
≤
x
≤
1
0
o.w.
f
Y
(
y
)
=
2
y
0
≤
y
≤
1
0
o.w.
Set up, but do not solve, the integral to compute the expected amount of
time that the one who arrives first must wait for the other person. Also,
what is
ρ
?
2. (Book Example 5.18) Let
X
and
Y
be discrete rv’s with joint pmf
p
(
x, y
) =
1
4
(
x, y
) = (

4
,
1)
,
(4
,
1)
,
(2
,
2)
,
(

2
,

2)
0
o.w.
What is the covariance of
X
and
Y
?
3. (Modified from book p.
212 # 41) Let
X
be the number of packages
being mailed to a randomly selected customer at a certain shipping facility.
Supposed the distribution of
X
is as follows:
x
1
2
3
p
(
x
)
.
5
.
3
.
2
(a) Consider a random sample of size
n
= 2 and let
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 Spring '08
 ALL
 Statistics, Probability, Probability theory, Alvie, book p.

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