STAT 225  Homework 7
Due Tuesday June 16
Comments:
1. This homework is due Tuesday, June 16 in class,
BEFORE
class starts.
2. Please remember
staple
if you turn in more than one page.
3. You must always SHOW ALL WORK. If you do not show your work, you may not receive
full credit.
Note: The text is using
Y
1
and
Y
2
instead of
X
and
Y
. Feel free to change to
X
and
Y
1. Page 242, problem 5.22
parts (a) and (b)
.
2. Page 252, problem 5.48
3. An urn contains 2 red balls and 3 white ones. 3 balls are taken out at random one after the
other with no replacement. Define:
X
 the number of white balls obtained after the first two balls are taken out.
Y
 the number of white balls obtained after all three balls are taken out.
(a) Derive the joint probability distribution of
X
and
Y
,
P
XY
(
x, y
), in a form of a table.
(b) Are
X
and
Y
independent? Justify your answer.
4. Consider the following joint pdf:
P
XY
(
x, y
) =
e

3
λ
λ
x
+
y
2
y
x
!
y
!
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 Summer '09
 TOM
 Probability distribution, probability density function, joint PDF, Marginal distribution, fX Y

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