This preview shows pages 1–2. Sign up to view the full content.
15B Weekly Quizzes
Fall 2000
Q1. A family has 4 girls and 3 boys.
(a) How many ways can they sit in a row?
(b) How many ways can they sit in a row if boys and girls must alternate?
Q2. How many ways can
t
teams each of size
s
be made from
st
people? The teams have
no names or other distinguishing features. Three versions were given depending on
student ID number:
s
=2
,t
=4;
s
=3
=3;
s
=4
.
Q3. Let
A
,
B
and
C
⊆
B
be sets. We make
B
A
into a probability space by selecting
functions from
A
to
B
uniformly at random.
(a) What is the probability that a random
f
is an injection?
(b) What is the probability that
f
(
A
)
⊆
C
for a random
f
?
Express answers in terms of
a
=

A

,
b
=

B

and
c
=

C

.
Q4. A permutation is given in cycle form. Write it in two line form and ﬁnd its tenth
power. Three versions were given depending on ID number.
(1
,
3
,
7)(2
,
9
,
4
,
8)(5
,
6)
(1
,
2
,
5
,
4)(3
,
9)(6
,
8
,
7)
(1
,
7)(2
,
4
,
9
,
6)(3
,
8
,
5)
.
Q5. Suppose
X
and
Y
are random variables with mean 0 and variance
σ
2
. Suppose that
Cov(
X, Y
)=
c
. Express the following in terms of
σ
and
c
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '01
 Bender
 Math

Click to edit the document details