251y063t 4/20/06
ECO251 QBA1
THIRD EXAM
Apr 25, 2005
TAKE HOME SECTION
Name: ____Computer Solution____
Student Number: _________________________
Throughout this exam show your work! Please indicate clearly what sections of the problem you are
answering and what formulas you are using.
Part III. Do all the Following (19+ Points) Show your work! Neatness counts!
1. Ben Horim and Levy present the following actual returns for stock in Republic Steel and General Foods
over a ten year period.
Year
R1
1
22.5
2
9.3
3 -18.6
4
48.1
5
44.4
6
56.0
7 -20.1
8 -11.0
9
17.1
10
22.3
R2
-23.7
8.6
4.3
-52.2
62.4
61.4
9.8
52.6
17.1
11.7
Before you start, personalize the data below as follows. Take the third to last digit of your student number
and subtract it from -52.2 in the R2 column. This will make the results for year 4 even more disappointing
than they actually were. (Example: Seymour Butz’s student number is 123450. He subtracts the 4 from
-52.2 getting -56.2) .
a) Find the sample mean, variance and coefficient of variation for R2. Use computational formulas.
The results must look as if you calculated them by hand, although it is perfectly reasonable to
check the results using a computer or a calculator. (2.5)
b) Find the sample covariance and correlation between R1 and R2. (3)
c) Using a conventional measure of risk, explain which stock is riskier. (1).
[6.5]
d) Make a table showing 11 portfolios. Start with a portfolio with all your money invested in stock 1
(P1 = 1, P2 = 0), then move to a portfolio with 90% in stock 1 and 10% in stock 2 (P1 = .90, P2 =
.10), and move by tenths until you get a portfolio that is all stock 2. (5). The table should look as
P1
R
s
C
1
.9
.8
.7
follows with much wider columns.
.6
.5
Here R is the weighted average return, s
.4
.3
.2
.1
0
is the standard deviation of the portfolio return, and C is the coefficient of variation.
[11.5]
1
251y063t 4/20/06
e)
f)
Make a graph . Put the mean return on the y axis and the standard deviation on the x axis. (3)
Connect your points in a curve. The C-like curve you will probably get illustrates the tradeoffs
between return and risk and is called an investment opportunities frontier.
Looking at the graph and the coefficients, are there stock portfolios that you would never
recommend? Why? What portfolio would you recommend to an 80-year old widow? Why? What
portfolio would you pick for yourself? Why? (1.5)
[16]
2. It’s time for a jorcillator problem! As everyone knows a jorcillator has two components, a Phillinx and a
Flubberall.
The life of a Phillinx, x , is described by a continuous uniform distribution between c  0  h5 and
d  30  h6 , where h5 and h6 are the last two digits of your student number .
The life of a Flubberall, y , is described by a Normal distribution with a mean of   20  h5 and a
standard deviation of   5.10 .
(Example: Seymour Butz’s student number is 123450. c  0  5  5 , d  30  0  30 and   20  5  25 ).
a)
Find the following probabilities for the Phillinx: (i) PPH 1   P0  x  10  , the probability that it
dies before the end of the tenth year, (ii) PPH 2   P10  x  20  , the probability that it dies
between the end of the tenth and the end of the twentieth year and (iii) PPH 3   P( x  20) , the
probability that it lasts beyond the twentieth year. (1.5)
b) Find the following probabilities for the Flubberall: (i) PF1   P0  y  10  , the probability that it
dies before the end of the tenth year, (ii) PF2   P10  y  20  , the probability that it dies
between the end of the tenth and the end of the twentieth year and (iii) PF3   P( y  20 ) , the
probability that it lasts beyond the twentieth year. (3)
c) Make a joint probability table using the 6 events described above. Assume independence. (1)
d) Assume that the Jorcillator will fail only if both components fail. Find the following probabilities
for the Jorcillator: (i) PJ 1  , the probability that it dies before the end of the tenth year, (ii)
PJ 2  , the probability that it dies between the end of the tenth and the end of the twentieth year
and (iii) PJ 3  , the probability that it lasts beyond the twentieth year. (3)
[23.5]
e)




(Extra credit) Find the following conditional probabilities: : (i) P J 3 F1 , (ii) P J 3 F2 (iii)
PJ 1 F3  , PF1 J 2  (2).
Computations for the portfolio problem and probabilities for the uniform and Normal distribution
follow.
2
251y063t 4/20/06
Computations for the Portfolio Problem
Version
0
Descriptive Statistics: R1
Variable
N N*
Mean
R1
10
0 17.00
Variable
R1
StDev
27.46
Minimum
-20.10
Q1
-12.90
Median
19.70
Q3
45.33
Maximum
56.00
Descriptive Statistics: R2
Variable
N N* Mean
R2
10
0 15.2
Data Display
Row
1
2
3
4
5
6
7
8
9
10
SE Mean
8.68
x
22.5
9.3
-18.6
48.1
44.4
56.0
-20.1
-11.0
17.1
22.3
xsq
506.25
86.49
345.96
2313.61
1971.36
3136.00
404.01
121.00
292.41
497.29
SE Mean
11.6
y
-23.7
8.6
4.3
-52.2
62.4
61.4
9.8
52.6
17.1
11.7
StDev
36.6
ysq
561.69
73.96
18.49
2724.84
3893.76
3769.96
96.04
2766.76
292.41
136.89
Minimum
-52.2
Q1
-2.7
Median
10.8
Q3
54.8
Maximum
62.4
xy
-533.25
79.98
-79.98
-2510.82
2770.56
3438.40
-196.98
-578.60
292.41
260.91
Data Display
sumx
sumx2
sumy
sumy2
sumxy
n
xbar
ybar
svarx
svary
scovxy
sx
sy
rxy
rxy2
170.000
9674.38
152.000
14334.8
2942.63
10.0000
17.0000
15.2000
753.820
1336.04
39.8478
27.4558
36.5519
0.0397063
0.00157659
Data Display
R1mean
R1stdv
R2mean
R2stdv
corr
17.0000
27.4558
15.2000
36.5519
0.0397063
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
Pin1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pmean
15.20
15.38
15.56
15.74
15.92
16.10
16.28
16.46
16.64
16.82
17.00
Pstdv
36.5519
33.1196
29.9662
27.1890
24.9141
23.2893
22.4559
22.5023
23.4230
25.1222
27.4558
CofV
2.40473
2.15342
1.92585
1.72738
1.56496
1.44654
1.37936
1.36709
1.40763
1.49359
1.61505
3
251y063t 4/20/06
Version
1.00000
Descriptive Statistics: R1
Variable
N N*
Mean
R1
10
0 17.00
Variable
R1
StDev
27.46
Minimum
-20.10
Q1
-12.90
Median
19.70
Q3
45.33
Maximum
56.00
Descriptive Statistics: R2
Variable
N N* Mean
R2
10
0 15.1
Data Display
Row
1
2
3
4
5
6
7
8
9
10
SE Mean
8.68
x
22.5
9.3
-18.6
48.1
44.4
56.0
-20.1
-11.0
17.1
22.3
xsq
506.25
86.49
345.96
2313.61
1971.36
3136.00
404.01
121.00
292.41
497.29
SE Mean
11.6
y
-23.7
8.6
4.3
-53.2
62.4
61.4
9.8
52.6
17.1
11.7
StDev
36.8
ysq
561.69
73.96
18.49
2830.24
3893.76
3769.96
96.04
2766.76
292.41
136.89
Minimum
-53.2
Q1
-2.7
Median
10.8
Q3
54.8
Maximum
62.4
xy
-533.25
79.98
-79.98
-2558.92
2770.56
3438.40
-196.98
-578.60
292.41
260.91
Data Display
sumx
sumx2
sumy
sumy2
sumxy
n
xbar
ybar
svarx
svary
scovxy
sx
sy
rxy
rxy2
170.000
9674.38
151.000
14440.2
2894.53
10.0000
17.0000
15.1000
753.820
1351.12
36.3922
27.4558
36.7576
0.0360601
0.00130033
Data Display
R1mean
R1stdv
R2mean
R2stdv
corr
17.0000
27.4558
15.1000
36.7576
0.0360601
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
Pin1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pmean
15.10
15.29
15.48
15.67
15.86
16.05
16.24
16.43
16.62
16.81
17.00
Pstdv
36.7576
33.2941
30.1084
27.2980
24.9897
23.3331
22.4727
22.5002
23.4123
25.1129
27.4558
CofV
2.43428
2.17751
1.94499
1.74205
1.57564
1.45377
1.38379
1.36946
1.40868
1.49392
1.61505
4
251y063t 4/20/06
Version
2.00000
Descriptive Statistics: R1
Variable
N N*
Mean
R1
10
0 17.00
Variable
R1
SE Mean
8.68
StDev
27.46
Minimum
-20.10
Q1
-12.90
Median
19.70
Q3
45.33
Maximum
56.00
Data Display
svar
12297.6
Descriptive Statistics: R2
Variable
N N* Mean
R2
10
0 15.0
Data Display
Row
1
2
3
4
5
6
7
8
9
10
x
22.5
9.3
-18.6
48.1
44.4
56.0
-20.1
-11.0
17.1
22.3
xsq
506.25
86.49
345.96
2313.61
1971.36
3136.00
404.01
121.00
292.41
497.29
SE Mean
11.7
y
-23.7
8.6
4.3
-54.2
62.4
61.4
9.8
52.6
17.1
11.7
StDev
37.0
ysq
561.69
73.96
18.49
2937.64
3893.76
3769.96
96.04
2766.76
292.41
136.89
Minimum
-54.2
Q1
-2.7
Median
10.8
Q3
54.8
Maximum
62.4
xy
-533.25
79.98
-79.98
-2607.02
2770.56
3438.40
-196.98
-578.60
292.41
260.91
Data Display
sumx
sumx2
sumy
sumy2
sumxy
n
xbar
ybar
svarx
svary
scovxy
sx
sy
rxy
rxy2
170.000
9674.38
150.000
14547.6
2846.43
10.0000
17.0000
15.0000
753.820
1366.40
32.9367
27.4558
36.9648
0.0324532
0.00105321
Data Display
R1mean
R1stdv
R2mean
R2stdv
corr
17.0000
27.4558
15.0000
36.9648
0.0324532
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
Pin1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pmean
15.0
15.2
15.4
15.6
15.8
16.0
16.2
16.4
16.6
16.8
17.0
Pstdv
36.9648
33.4701
30.2521
27.4083
25.0664
23.3778
22.4902
22.4985
23.4017
25.1035
27.4558
CofV
2.46432
2.20198
1.96442
1.75694
1.58648
1.46111
1.38828
1.37186
1.40974
1.49426
1.61505
5
251y063t 4/20/06
Version
3.00000
Descriptive Statistics: R1
Variable
N N*
Mean
R1
10
0 17.00
Variable
R1
StDev
27.46
Minimum
-20.10
Q1
-12.90
Median
19.70
Q3
45.33
Maximum
56.00
Descriptive Statistics: R2
Variable
N N* Mean
R2
10
0 14.9
Data Display
Row
1
2
3
4
5
6
7
8
9
10
SE Mean
8.68
x
22.5
9.3
-18.6
48.1
44.4
56.0
-20.1
-11.0
17.1
22.3
xsq
506.25
86.49
345.96
2313.61
1971.36
3136.00
404.01
121.00
292.41
497.29
SE Mean
11.8
y
-23.7
8.6
4.3
-55.2
62.4
61.4
9.8
52.6
17.1
11.7
StDev
37.2
ysq
561.69
73.96
18.49
3047.04
3893.76
3769.96
96.04
2766.76
292.41
136.89
Minimum
-55.2
Q1
-2.7
Median
10.8
Q3
54.8
Maximum
62.4
xy
-533.25
79.98
-79.98
-2655.12
2770.56
3438.40
-196.98
-578.60
292.41
260.91
Data Display
sumx
sumx2
sumy
sumy2
sumxy
n
xbar
ybar
svarx
svary
scovxy
sx
sy
rxy
rxy2
170.000
9674.38
149.000
14657.0
2798.33
10.0000
17.0000
14.9000
753.820
1381.88
29.4811
27.4558
37.1736
0.0288852
0.000834354
Data Display
R1mean
R1stdv
R2mean
R2stdv
corr
17.0000
27.4558
14.9000
37.1736
0.0288852
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
Pin1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pmean
14.90
15.11
15.32
15.53
15.74
15.95
16.16
16.37
16.58
16.79
17.00
Pstdv
37.1736
33.6477
30.3972
27.5199
25.1443
23.4236
22.5084
22.4972
23.3913
25.0942
27.4558
CofV
2.49487
2.22685
1.98415
1.77205
1.59748
1.46856
1.39284
1.37429
1.41082
1.49459
1.61505
6
251y063t 4/20/06
Version
4.00000
Descriptive Statistics: R1
Variable
N N*
Mean
R1
10
0 17.00
Variable
R1
StDev
27.46
Minimum
-20.10
Q1
-12.90
Median
19.70
Q3
45.33
Maximum
56.00
Descriptive Statistics: R2
Variable
N N* Mean
R2
10
0 14.8
Data Display
Row
1
2
3
4
5
6
7
8
9
10
SE Mean
8.68
x
22.5
9.3
-18.6
48.1
44.4
56.0
-20.1
-11.0
17.1
22.3
xsq
506.25
86.49
345.96
2313.61
1971.36
3136.00
404.01
121.00
292.41
497.29
SE Mean
11.8
y
-23.7
8.6
4.3
-56.2
62.4
61.4
9.8
52.6
17.1
11.7
StDev
37.4
ysq
561.69
73.96
18.49
3158.44
3893.76
3769.96
96.04
2766.76
292.41
136.89
Minimum
-56.2
Q1
-2.7
Median
10.8
Q3
54.8
Maximum
62.4
xy
-533.25
79.98
-79.98
-2703.22
2770.56
3438.40
-196.98
-578.60
292.41
260.91
Data Display
sumx
sumx2
sumy
sumy2
sumxy
n
xbar
ybar
svarx
svary
scovxy
sx
sy
rxy
rxy2
170.000
9674.38
148.000
14768.4
2750.23
10.0000
17.0000
14.8000
753.820
1397.56
26.0256
27.4558
37.3839
0.0253561
0.000642929
Data Display
R1mean
R1stdv
R2mean
R2stdv
corr
17.0000
27.4558
14.8000
37.3839
0.0253561
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
Pin1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pmean
14.80
15.02
15.24
15.46
15.68
15.90
16.12
16.34
16.56
16.78
17.00
Pstdv
37.3839
33.8267
30.5437
27.6329
25.2235
23.4703
22.5272
22.4963
23.3811
25.0849
27.4558
CofV
2.52594
2.25211
2.00418
1.78738
1.60864
1.47612
1.39747
1.37676
1.41190
1.49493
1.61505
7
251y063t 4/20/06
Version
5.00000
Descriptive Statistics: R1
Variable
N N*
Mean
R1
10
0 17.00
Variable
R1
StDev
27.46
Minimum
-20.10
Q1
-12.90
Median
19.70
Q3
45.33
Maximum
56.00
Descriptive Statistics: R2
Variable
N N* Mean
R2
10
0 14.7
Data Display
Row
1
2
3
4
5
6
7
8
9
10
SE Mean
8.68
x
22.5
9.3
-18.6
48.1
44.4
56.0
-20.1
-11.0
17.1
22.3
xsq
506.25
86.49
345.96
2313.61
1971.36
3136.00
404.01
121.00
292.41
497.29
SE Mean
11.9
y
-23.7
8.6
4.3
-57.2
62.4
61.4
9.8
52.6
17.1
11.7
StDev
37.6
ysq
561.69
73.96
18.49
3271.84
3893.76
3769.96
96.04
2766.76
292.41
136.89
Minimum
-57.2
Q1
-2.7
Median
10.8
Q3
54.8
Maximum
62.4
xy
-533.25
79.98
-79.98
-2751.32
2770.56
3438.40
-196.98
-578.60
292.41
260.91
Data Display
sumx
sumx2
sumy
sumy2
sumxy
n
xbar
ybar
svarx
svary
scovxy
sx
sy
rxy
rxy2
170.000
9674.38
147.000
14881.8
2702.13
10.0000
17.0000
14.7000
753.820
1413.43
22.5700
27.4558
37.5957
0.0218655
0.000478102
Data Display
R1mean
R1stdv
R2mean
R2stdv
corr
17.0000
27.4558
14.7000
37.5957
0.0218655
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
Pin1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pmean
14.70
14.93
15.16
15.39
15.62
15.85
16.08
16.31
16.54
16.77
17.00
Pstdv
37.5957
34.0071
30.6916
27.7472
25.3038
23.5180
22.5468
22.4958
23.3710
25.0757
27.4558
CofV
2.55753
2.27777
2.02451
1.80294
1.61996
1.48379
1.40216
1.37926
1.41300
1.49527
1.61505
8
251y063t 4/20/06
Version
6.00000
Descriptive Statistics: R1
Variable
N N*
Mean
R1
10
0 17.00
Variable
R1
StDev
27.46
Minimum
-20.10
Q1
-12.90
Median
19.70
Q3
45.33
Maximum
56.00
Descriptive Statistics: R2
Variable
N N* Mean
R2
10
0 14.6
Data Display
Row
1
2
3
4
5
6
7
8
9
10
SE Mean
8.68
x
22.5
9.3
-18.6
48.1
44.4
56.0
-20.1
-11.0
17.1
22.3
xsq
506.25
86.49
345.96
2313.61
1971.36
3136.00
404.01
121.00
292.41
497.29
SE Mean
12.0
y
-23.7
8.6
4.3
-58.2
62.4
61.4
9.8
52.6
17.1
11.7
StDev
37.8
ysq
561.69
73.96
18.49
3387.24
3893.76
3769.96
96.04
2766.76
292.41
136.89
Minimum
-58.2
Q1
-2.7
Median
10.8
Q3
54.8
Maximum
62.4
xy
-533.25
79.98
-79.98
-2799.42
2770.56
3438.40
-196.98
-578.60
292.41
260.91
Data Display
sumx
sumx2
sumy
sumy2
sumxy
n
xbar
ybar
svarx
svary
scovxy
sx
sy
rxy
rxy2
170.000
9674.38
146.000
14997.2
2654.03
10.0000
17.0000
14.6000
753.820
1429.51
19.1144
27.4558
37.8089
0.0184134
0.000339053
Data Display
R1mean
R1stdv
R2mean
R2stdv
corr
17.0000
27.4558
14.6000
37.8089
0.0184134
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
Pin1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pmean
14.60
14.84
15.08
15.32
15.56
15.80
16.04
16.28
16.52
16.76
17.00
Pstdv
37.8089
34.1889
30.8408
27.8627
25.3852
23.5667
22.5671
22.4957
23.3611
25.0665
27.4558
CofV
2.58965
2.30384
2.04515
1.81872
1.63144
1.49156
1.40692
1.38180
1.41411
1.49562
1.61505
9
251y063t 4/20/06
Version
7.00000
Descriptive Statistics: R1
Variable
R1
N
10
N*
0
Variable
R1
Maximum
56.00
Mean
17.00
SE Mean
8.68
Descriptive Statistics: R2
Variable
R2
N
10
N*
0
Mean
14.5
Data Display
Row
1
2
3
4
5
6
7
8
9
10
x
22.5
9.3
-18.6
48.1
44.4
56.0
-20.1
-11.0
17.1
22.3
xsq
506.25
86.49
345.96
2313.61
1971.36
3136.00
404.01
121.00
292.41
497.29
SE Mean
12.0
y
-23.7
8.6
4.3
-59.2
62.4
61.4
9.8
52.6
17.1
11.7
StDev
27.46
StDev
38.0
ysq
561.69
73.96
18.49
3504.64
3893.76
3769.96
96.04
2766.76
292.41
136.89
Minimum
-20.10
Minimum
-59.2
Q1
-12.90
Q1
-2.7
Median
19.70
Median
10.8
Q3
45.33
Q3
54.8
Maximum
62.4
xy
-533.25
79.98
-79.98
-2847.52
2770.56
3438.40
-196.98
-578.60
292.41
260.91
Data Display
sumx
sumx2
sumy
sumy2
sumxy
n
xbar
ybar
svarx
svary
scovxy
sx
sy
rxy
rxy2
170.000
9674.38
145.000
15114.6
2605.93
10.0000
17.0000
14.5000
753.820
1445.79
15.6589
27.4558
38.0235
0.0149994
0.000224983
Data Display
R1mean
R1stdv
R2mean
R2stdv
corr
17.0000
27.4558
14.5000
38.0235
0.0149994
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
Pin1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pmean
14.50
14.75
15.00
15.25
15.50
15.75
16.00
16.25
16.50
16.75
17.00
Pstdv
38.0235
34.3722
30.9914
27.9796
25.4679
23.6163
22.5880
22.4960
23.3514
25.0573
27.4558
CofV
2.62231
2.33032
2.06610
1.83473
1.64309
1.49945
1.41175
1.38437
1.41524
1.49596
1.61505
10
251y063t 4/20/06
Version
8.00000
Descriptive Statistics: R1
Variable
N N*
Mean
R1
10
0 17.00
Variable
R1
StDev
27.46
Minimum
-20.10
Q1
-12.90
Median
19.70
Q3
45.33
Maximum
56.00
Descriptive Statistics: R1
Variable
N N* Mean
R1
10
0 14.4
Data Display
Row
1
2
3
4
5
6
7
8
9
10
SE Mean
8.68
x
22.5
9.3
-18.6
48.1
44.4
56.0
-20.1
-11.0
17.1
22.3
xsq
506.25
86.49
345.96
2313.61
1971.36
3136.00
404.01
121.00
292.41
497.29
SE Mean
12.1
y
-23.7
8.6
4.3
-60.2
62.4
61.4
9.8
52.6
17.1
11.7
StDev
38.2
ysq
561.69
73.96
18.49
3624.04
3893.76
3769.96
96.04
2766.76
292.41
136.89
Minimum
-60.2
Q1
-2.7
Median
10.8
Q3
54.8
Maximum
62.4
xy
-533.25
79.98
-79.98
-2895.62
2770.56
3438.40
-196.98
-578.60
292.41
260.91
Data Display
sumx
sumx2
sumy
sumy2
sumxy
n
xbar
ybar
svarx
svary
scovxy
sx
sy
rxy
rxy2
170.000
9674.38
144.000
15234.0
2557.83
10.0000
17.0000
14.4000
753.820
1462.27
12.2033
27.4558
38.2396
0.0116234
0.000135102
Data Display
R1mean
R1stdv
R2mean
R2stdv
corr
17.0000
27.4558
14.4000
38.2396
0.0116234
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
Pin1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pmean
14.40
14.66
14.92
15.18
15.44
15.70
15.96
16.22
16.48
16.74
17.00
Pstdv
38.2396
34.5568
31.1434
28.0977
25.5516
23.6669
22.6096
22.4967
23.3418
25.0482
27.4558
CofV
2.65553
2.35722
2.08736
1.85097
1.65490
1.50745
1.41664
1.38697
1.41637
1.49631
1.61505
11
251y063t 4/20/06
Version
9.00000
Descriptive Statistics: R1
Variable
N N*
Mean
R1
10
0 17.00
Variable
R1
StDev
27.46
Minimum
-20.10
Q1
-12.90
Median
19.70
Q3
45.33
Maximum
56.00
Descriptive Statistics: R1
Variable
N N* Mean
R1
10
0 14.3
Data Display
Row
1
2
3
4
5
6
7
8
9
10
SE Mean
8.68
x
22.5
9.3
-18.6
48.1
44.4
56.0
-20.1
-11.0
17.1
22.3
xsq
506.25
86.49
345.96
2313.61
1971.36
3136.00
404.01
121.00
292.41
497.29
SE Mean
12.2
y
-23.7
8.6
4.3
-61.2
62.4
61.4
9.8
52.6
17.1
11.7
StDev
38.5
ysq
561.69
73.96
18.49
3745.44
3893.76
3769.96
96.04
2766.76
292.41
136.89
Minimum
-61.2
Q1
-2.7
Median
10.8
Q3
54.8
Maximum
62.4
xy
-533.25
79.98
-79.98
-2943.72
2770.56
3438.40
-196.98
-578.60
292.41
260.91
Data Display
sumx
sumx2
sumy
sumy2
sumxy
n
xbar
ybar
svarx
svary
scovxy
sx
sy
rxy
rxy2
170.000
9674.38
143.000
15355.4
2509.73
10.0000
17.0000
14.3000
753.820
1478.94
8.74778
27.4558
38.4570
0.00828491
0.000068640
Data Display
R1mean
R1stdv
R2mean
R2stdv
corr
17.0000
27.4558
14.3000
38.4570
0.00828491
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
Pin1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Pmean
14.30
14.57
14.84
15.11
15.38
15.65
15.92
16.19
16.46
16.73
17.00
Pstdv
38.4570
34.7427
31.2966
28.2170
25.6365
23.7185
22.6320
22.4978
23.3324
25.0391
27.4558
CofV
2.68930
2.38454
2.10893
1.86744
1.66687
1.51556
1.42161
1.38961
1.41752
1.49666
1.61505
12
251y063t 4/20/06
Probabilities for the Uniform Distribution
Version number is h5 h6
Data Display
version
P00-10
P10-20
P20-30
Psum
00
0.333333
0.333333
0.333333
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
01.00000
0.344828
0.344828
0.310345
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
02.00000
0.357143
0.357143
0.285714
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
03.00000
0.370370
0.370370
0.259259
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
04.00000
0.384615
0.384615
0.230769
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
05.00000
0.400000
0.400000
0.200000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
06.00000
0.416667
0.416667
0.166667
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
07.00000
0.434783
0.434783
0.130435
1.00000
13
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
08.00000
0.454545
0.454545
0.0909091
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
09.00000
0.476190
0.476190
0.0476190
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
10.0000
0.310345
0.344828
0.344828
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
11.0000
0.321429
0.357143
0.321429
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
12.0000
0.333333
0.370370
0.296296
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
13.0000
0.346154
0.384615
0.269231
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
14.0000
0.360000
0.400000
0.240000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
15.0000
0.375000
0.416667
0.208333
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
16.0000
0.391304
0.434783
0.173913
1.00000
14
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
17.0000
0.409091
0.454545
0.136364
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
18.0000
0.428571
0.476190
0.0952381
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
19.0000
0.450000
0.500000
0.0500000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
20.0000
0.285714
0.357143
0.357143
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
21.0000
0.296296
0.370370
0.333333
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
22.0000
0.307692
0.384615
0.307692
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
23.0000
0.320000
0.400000
0.280000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
24.0000
0.333333
0.416667
0.250000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
25.0000
0.347826
0.434783
0.217391
1.00000
15
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
26.0000
0.363636
0.454545
0.181818
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
27.0000
0.380952
0.476190
0.142857
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
28.0000
0.400000
0.500000
0.100000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
29.0000
0.421053
0.526316
0.0526316
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
30.0000
0.259259
0.370370
0.370370
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
31.0000
0.269231
0.384615
0.346154
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
32.0000
0.280000
0.400000
0.320000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
33.0000
0.291667
0.416667
0.291667
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
34.0000
0.304348
0.434783
0.260870
1.00000
16
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
35.0000
0.318182
0.454545
0.227273
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
36.0000
0.333333
0.476190
0.190476
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
37.0000
0.350000
0.500000
0.150000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
38.0000
0.368421
0.526316
0.105263
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
39.0000
0.388889
0.555556
0.0555556
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
40.0000
0.230769
0.384615
0.384615
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
41.0000
0.240000
0.400000
0.360000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
42.0000
0.250000
0.416667
0.333333
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
43.0000
0.260870
0.434783
0.304348
1.00000
17
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
44.0000
0.272727
0.454545
0.272727
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
45.0000
0.285714
0.476190
0.238095
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
46.0000
0.300000
0.500000
0.200000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
47.0000
0.315789
0.526316
0.157895
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
48.0000
0.333333
0.555556
0.111111
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
49.0000
0.352941
0.588235
0.0588235
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
50.0000
0.200000
0.400000
0.400000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
51.0000
0.208333
0.416667
0.375000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
52.0000
0.217391
0.434783
0.347826
1.00000
18
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
53.0000
0.227273
0.454545
0.318182
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
54.0000
0.238095
0.476190
0.285714
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
55.0000
0.250000
0.500000
0.250000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
56.0000
0.263158
0.526316
0.210526
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
57.0000
0.277778
0.555556
0.166667
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
58.0000
0.294118
0.588235
0.117647
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
59.0000
0.312500
0.625000
0.0625000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
60.0000
0.166667
0.416667
0.416667
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
61.0000
0.173913
0.434783
0.391304
1.00000
19
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
62.0000
0.181818
0.454545
0.363636
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
63.0000
0.190476
0.476190
0.333333
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
64.0000
0.200000
0.500000
0.300000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
65.0000
0.210526
0.526316
0.263158
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
66.0000
0.222222
0.555556
0.222222
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
67.0000
0.235294
0.588235
0.176471
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
68.0000
0.250000
0.625000
0.125000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
69.0000
0.266667
0.666667
0.0666667
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
70.0000
0.130435
0.434783
0.434783
1.00000
20
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
71.0000
0.136364
0.454545
0.409091
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
72.0000
0.142857
0.476190
0.380952
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
73.0000
0.150000
0.500000
0.350000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
74.0000
0.157895
0.526316
0.315789
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
75.0000
0.166667
0.555556
0.277778
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
76.0000
0.176471
0.588235
0.235294
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
77.0000
0.187500
0.625000
0.187500
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
78.0000
0.200000
0.666667
0.133333
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
79.0000
0.214286
0.714286
0.0714286
1.00000
21
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
80.0000
0.0909091
0.454545
0.454545
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
81.0000
0.0952381
0.476190
0.428571
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
82.0000
0.100000
0.500000
0.400000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
83.0000
0.105263
0.526316
0.368421
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
84.0000
0.111111
0.555556
0.333333
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
85.0000
0.117647
0.588235
0.294118
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
86.0000
0.125000
0.625000
0.250000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
87.0000
0.133333
0.666667
0.200000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
88.0000
0.142857
0.714286
0.142857
1.00000
22
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
89.0000
0.153846
0.769231
0.0769231
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
90.0000
0.0476190
0.476190
0.476190
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
91.0000
0.0500000
0.500000
0.450000
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
92.0000
0.0526316
0.526316
0.421053
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
93.0000
0.0555556
0.555556
0.388889
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
94.0000
0.0588235
0.588235
0.352941
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
95.0000
0.0625000
0.625000
0.312500
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
96.0000
0.0666667
0.666667
0.266667
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
97.0000
0.0714286
0.714286
0.214286
1.00000
23
251y063t 4/20/06
Data Display
version
P00-10
P10-20
P20-30
Psum
98.0000
0.0769231
0.769231
0.153846
1.00000
Data Display
version
P00-10
P10-20
P20-30
Psum
99.0000
0.0833333
0.833333
0.0833333
1.00000
24
251y063t 4/20/06
Probabilities for the Normal Distribution
Data Display
Row mean var lower upper
1
20 5.1
0
10
2
20 5.1
10
20
3
20 5.1
20
50
Sum of prob = 0.999956
prob
0.024908
0.475048
0.500000
Data Display
Row mean var lower upper
1
21 5.1
0
10
2
21 5.1
10
20
3
21 5.1
20
50
Sum of prob = 0.999981
prob
0.015489
0.406766
0.577726
Data Display
Row mean var lower
1
22 5.1
0
2
22 5.1
10
3
22 5.1
20
Sum of prob = 0.99999
upper
10
20
50
prob
0.009305
0.338158
0.652529
Data Display
Row mean var lower
1
23 5.1
0
2
23 5.1
10
3
23 5.1
20
Sum of prob = 1.00000
upper
10
20
50
prob
0.005398
0.272786
0.721813
Data Display
Row mean var lower
1
24 5.1
0
2
24 5.1
10
3
24 5.1
20
Sum of prob = 1.00000
upper
10
20
50
prob
0.003023
0.213403
0.783572
Data Display
Row mean var lower
1
25 5.1
0
2
25 5.1
10
3
25 5.1
20
Sum of prob = 1.00000
upper
10
20
50
prob
0.001634
0.161811
0.836553
Data Display
Row mean var lower
1
26 5.1
0
2
26 5.1
10
3
26 5.1
20
Sum of prob = 1.00000
upper
10
20
50
prob
0.000853
0.118851
0.880295
Data Display
Row mean var lower
1
27 5.1
0
2
27 5.1
10
3
27 5.1
20
Sum of prob = 1.00000
upper
10
20
50
prob
0.000429
0.084517
0.915050
25
251y063t 4/20/06
Data Display
Row mean var lower
1
28 5.1
0
2
28 5.1
10
3
28 5.1
20
Sum of prob = 0.99999
upper
10
20
50
prob
0.000208
0.058159
0.941625
Data Display
Row mean var lower upper
1
29 5.1
0
10
2
29 5.1
10
20
3
29 5.1
20
50
Sum of prob = 0.999981
prob
0.000097
0.038709
0.961174
26