Sta(r400
Test
2
3-13-89
B.
Kellogg
Section
0401
1.
An
urn
contains
n
~
6
+
w
balls,
6
of
which
are
black
and
w
of
which are
white.
A
ball
is
removed.
Then
a
second
ball
is
removed.
Let
Xi
=
1
if the
»-th
ball
is
black,
0
if
the
t'-th
ball
is
white.
»
=
1,2.
Find
d],
Var(A',),
Cov(A'
1)
A
:!
).
2.
Let
AT
be
a
random
variable
with
density
function
z
<0.
Calculate
P(X
>
a).
Using
Markov's
inequality,
find
an
upper
bound
for
P(X
>
a).
Compare
these
two
quantities
for
large
a.
3.
Let
A"
be
a
random
variable
whose
density
function
is
given
by
0,
x<-a,
^(i-fy).
-a<x<a,
(0,
a<x.
Find
E[X}
and
Var(A').
Find
the
distribution
function
F(x).
Sketch
a
graph
of
f(x)
and
discuss
how
the
graph,
and the
variance,
depend
on
a.
4.
A
door
to
door
salesman
makes
on
the
average
1
sale
every
20
house
calls.
In
a
day
he
mak<:s
50
house
calls.
What
is
the
probability
of
his
making
at
least
2
sales
during
the
day?
5.
A
casino
offers
a
^Hue-game
consisting
of
throwing
a pair
of
dice.
It
costs
So.00
to
play
the
game,
and
if
the
pair
of
dice
show
z.
seven,
the
player
collects
$25.
Is
it
wise
for
the
casino
to
offer
this
payoff?
If
the
game
is
played
1000
times per
day,
what
is
the
expected
daily
profit
or
loss?
&
30
T