251grass2-08b
6/12/08 (Open this document in 'Page Layout' view!)
Graded Assignment 2
Name:
There will be a penalty for papers that are unstapled. 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).
x
4
x
1
.10
5
.05
6
0
y 2
.05
.30
0
3
0
0
.50
and
4
1
0
5
.05
6
.10
y 2
0
.30
.05
3 .50
0
0
1) Use the joint probability tables above.
For these joint probability tables (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. (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
80
52
77
59
87
45
72
61
80
54
84
56
83
67
87
63
92
53
77