Math 431 Final Exam
Room B130, May 10, 2004, 2:45pm
M´arton Bal´azs
NAME:
1.
(40 points) For the magicball team of Wonderland, 30 persons are chosen out of the several
million citizens. In Wonderland, there are only 10 names, and each of these names is given to
1/10 part of the population. Use indicator variables to compute the expected number of di±erent
names in the team. What assumptions are you making?
Bonus Problem:
(10 points) Compute the standard deviation of the number of di±erent names
in the team.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Let
X
and
Y
be the two coordinates of a point uniformly chosen in the triangle with vertices
(0
,
0), (1
,
1) and (

1
,
1). (In other words: the point (
X, Y
) is uniformly chosen in the set
{
(
x, y
) : 0
≤
y
≤
1
,

y
≤
x
≤
y
}
.) Compute
(a)
(15 points)
E
(
X
),
E
(
Y
),
(b)
(15 points) the correlation of
X
and
Y
,
(c)
(15 points) the conditional expectations
E
(
X

Y
=
y
) and
E
(
Y

X
=
x
).
If you solve this by integration, make sure you take into account the appropriate limits of the
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 BALAZS
 Math, Probability, Standard Deviation, Variance, Probability theory

Click to edit the document details