3/5/07 251grass2
(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 from now on 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 an
old exam (as well as an old exam with no name on it that the perp will not admit responsibility for).
1) Use the second joint probability table in Problem K4. 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 not change.
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 following data represent the scores of a group of students on a math placement test and their grades
in a math course. Personalize the data by subtracting the second to last digit of your student number from
the 45 in the x column. (i) Compute the sample mean and variance 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) 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 .
Test Score
Grades
y
x
51
75
52
72
59
82
45
67
61
75
54
79
56
78
67
82
63
87
53
72
60
96