I
25.5.
The net
winnings
for
the
company
are:
$0
with
probabitity
3/b
l"
llq
case
that
thev do not win the
bid;
$2
million
with
probability
(2/5)(2/3) if
they
win
the bid
and
do not find
oil;
or
$4
million
with
prob
abilitv (215)(l/3)
if
they win the bid
and do
find
oil.
The expectation
of
the net
winnings is therefore
/4\/
48
\
Yar(I()
:
02
:
EIK2I

tt,
:
I
tr
toltuio'

(0.ss5)2
4T
<'J*
,
iL
lc:o
(Y)
{t
*
lE
73
:
0'475o'148:0'327'
0(3/5)

2(4/15)
*
4(2
/r5]
:
o.
2.5.7.
(SA)
If
tr(
:
number
of
kings
in
the
hand,
then
Note
that
the
first
term
does
not
contribute anything
to
the
value.
Therefore,
the
terms
of
the
above sum can
be
evaluated
explicitly
for
k
:
1,2,3,
and
4.
The
answer
is 0.385. For
the
'rariance.
Adf
2.5.8.
db
)l
,9,bU*

b)rl
:
2Elx

bl
:
2(Elxl
b)
:
o
+
b:
ElXl.
Since
the
""cooh
deri'vative
with
respect
to
b
is 2
>
O,
we have a
minimum'
2.5.L2.If
rr
is
the
dollar amount
invested
in
the
first
asset,
then
(1000

c1)
will
be
invested
iu
the second.
Let
R1 and
R2 be
the
two
random
t"i"s
of
return.
R1
has mean
pr
:
'05
and
variance
o?
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 Spring '08
 Moumen,F
 Probability, Trigraph, PIS, net winnings, toltuio, critical point c1, frrarginal mass function

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