251grass2-081
3/6/08
(Open this document in 'Page Layout' view!) Graded Assignment 2
Name:
Class days and time:
Student number:
There will be a penalty for papers that are unstapled or do not have the three information items
requested above. Note that neatness means paper neatly trimmed on the left side if it has been torn,
multiple pages stapled and paper written on only one side. The stapling is for your protection –
putting your name on every page helps too, I still have some unclaimed pages from old papers. Make
copies of your work before you hand it in.
1) Use the joint probability table below, which resembles the table in Problem K4. You will find a solved
problem somewhat like this in 251solnK0.
x
4
5
1
0
0
6
.40
y 2
0
.20
0
3 .40
0
0
Modify the table as follows: subtract the last digit of your student number (divided by 100) from all three
numbers on the diagonal, add the same number to any 3 numbers off the diagonal, if the last digit of your
student number is zero, use 10. For example, if the last two digits of your number are 30, the .40 on the
diagonal becomes .40 - .10 = .30 and a zero will become .10. The sum of the numbers in the table will still
be one.
For this joint probability table (i) check for independence, (ii) Compute E x  and Varx  , (iii) Compute
 
 
Covx, y  or  xy and Corr x, y  or  xy , (iv) Compute Ex  y  and Var x  y  from the results in (ii)
and (iii), (iv) Compute Cov3x  3, y  and Corr 3x  3, y  using the formulas in section K4 of 251v2out
or section C1 of 251var2. Note that y  1y  0 .
2) The PHLX Gold/Silver SectorSM (XAUSM) is a capitalization-weighted index composed of 16 companies
involved in the gold and silver mining industry. XAU was set to an initial value of 100 in January 1979;
options commenced trading on December 19, 1983. The Dow-Jones Utility average is an average based on
the prices of 16 (I think) utility stocks. Both gold and utilities can attract cautious investors under certain
stock market conditions, so it is interesting to look at how they move relative to one another. The values of
these two indices for 20 very recent trading days are given on the next page.
251grass2-081
3/6/08
x
Row pick Date
1
* 03/05
2
* 03/04
3
* 03/03
4
* 02/29
5
* 02/28
6
* 02/27
7
* 02/26
8
* 02/25
9
* 02/22
10
* 02/21
11
0 02/20
12
1 02/19
13
2 02/15
14
3 02/14
15
4 02/13
16
5 02/12
17
6 02/11
18
7 02/08
19
8 02/07
20
9 02/06
PHLXGS
203.32
195.62
202.98
196.58
202.84
197.84
193.13
188.12
189.94
196.56
189.56
186.10
177.32
176.87
179.43
176.65
182.06
181.25
174.88
129.98
y
DJUT
496.60
489.97
482.76
477.50
492.40
496.04
504.63
500.78
497.54
491.82
499.95
499.85
500.41
498.79
504.05
502.08
497.90
494.39
496.96
498.66
You are expected to work with 11 of the 20 observations shown above. Use the first 10 rows of data and
pick one more row by finding the row marked with the second-to-last digit of your student number. (i)
Compute the sample mean and standard deviation of x , (ii) Compute Covx, y  or s xy and Corr x, y  or
rxy , (iii) Compute the sample mean and variance of
x  y 
from the results in (i) and (ii). (iv) The
coefficient of variation is computed by dividing the standard deviation by the mean. Compute a coefficient
of variation for x , y and x  y and compare the relative safety of investing in precious metal stocks,
investing in utilities and doing both. (v) Just for practice, compute Cov6 x  3, y  and Corr 6 x  3, y 
using the formulas in section K4 of 251v2out or section C1 of 251var2. Note that y  1y  0 .