4.29
Expected profits are highest for Strategy 1 at $650 vs. $550 for Strategy 2 and
$400 for Strategy 3. The strategy to recommend would depend on the risk
aversion of the investor. The variability of Strategy 1 is much higher than
the variability of Strategy 2. The standard deviation of Strategy 1 is
$3,927.7856 vs. $567.89 for Strategy 2. Many risk averse investors would
likely adopt Strategy 2 with its lower standard deviation and hence, lower risk.
4.45
 x = 2.0 sales
4.83
OR
 x = np = 5(.4) = 2.0 sales
a.
Joint cumulative probability function at X = 1, Y = 4:
FX,Y(1,4) = .09 + .07 + .14 + .23 = .53
b.
PY|X(3|0) = .09/.19 = .4737
PY|X(4|0) = .07/.19 = .3684
PY|X(5|0) = .03/.19 = .1579
c.
PX|Y(0|4) = .07/.46 = .1522
PX|Y(1|4) = .23/.46 = .5
PX|Y(2|4) = .16/.46 = .3478
d.
E(XY) = 0 + 1(3)(.14) + 1(4)(.23) + 1(5)(.10) + 2(3)(.07) + 2(4)(.16) +
2(5)(.11)
= 4.64
 x  0  .47  2(.34)  1.15
 y  3(.3)  4(.46)  5(.24)  3.94
Cov( X , Y )  4.64  (1.15)(3.94) = .109
The covariance indicates that there is a positive association between the
number of lines in the advertisement and the volume of inquiries.
e.
No, because Cov ( X , Y )  0
X Return
Y Return
P(x)
Mean of X
Var of X
StDev of X
0
1
2
P(y) Mean of Y
3
0.09
0.14
0.07
0.3
4
0.07
0.23
0.16
0.46
1.84 0.001656
5
0.03
0.1
0.11
0.24
1.2 0.269664
0.19
0.47
0.34
0
0.47
0.68
1.15
0.251275 0.010575 0.24565
0.5075
0.9
3.94
0.4956309
5.37
180  200
< Z < 0) = .5 – [1- Fz (1)] = .5 -.1587 = .3413
20
245  200
b. P(Z >
) = 1 – FZ(2.25) = .0122
20
c. Smaller
a. P(
Var of Y StDev of Y
0.26508
0.5364
0.732393
d. P(Z < -1.28) = .1, -1.28 =
Xi  200
,
20
Xi = 174.4
5.45
a.
E[X] =  = 400(.1) = 40,  =
(400)(.1)(.9) = 6
35  40
) = P(Z > -.83) = FZ(.83) = .7967
6
40  40
50  40
b. P(
<Z<
) = P(0 < Z < 1.67) = Fz (1.67) – FZ(0)
6
6
= 9525 - .5 = .4525
34  40
48  40
c. P(
<Z<
) = P(-1 < Z < 1.33)
6
6
= Fz (1.33) – [1 – FZ(1)] = .9082 - .1587 = .7495
d. 40 - 41
P(Z >
5.75
W = aX – bY = 10X – 4Y
W  a  x  b y = 10(400) – 4(400) = 2400
 2W  a 2 2 X  b 2 2Y  2abCorr ( X , Y ) X  Y
=102(900) + 42(1600) – 2(10)(4)(.5)(30)(40) = 67,600
 W  67, 600 =260
2000  2400
) = P(Z > -1.54) = FZ(1.54) = .9382
260
P(Z >
6.23
a.  x 
300, 000 400
= 26,859,689
499
100
b. P(Z >
825, 000  800, 000
)= P(Z > .93) = .1762
26,859.689
c. P(Z >
780, 000  800, 000
)= P(Z > -.74) = .7704
26,859.689
d. P(
790, 000  800, 000
820, 000  800, 000
)
<Z<
26,859.689
26,859.689
= P(-.37 < Z < .74) = .4147
6.35
a.
 pˆ 
(.42)(.58)
= .0285
300
.5  .42
)= P(Z > 2.81) = .0025
.0285
.4  .42
.45  .42
c. P(
<Z<
)= P(-.7 < Z < 1.05) = .6111
.0285
.0285
d. .41 - .43
b.
P(Z >