PROBLEM 9E
A car dealer sells X cars each day and always tries to sell an extended warranty on each of these cars. (In our opinion, most of these warranties are not good deals.) Let Y be the number of extended warranties sold; then Y ≤ X. The joint pmf of X and Y is given by
(a) Find the value of c.
(b) Sketch the support of X and Y.
(c) Record the marginal pmfs fX(x) and fY(y) in the “margins.”
(d) Are X and Y independent?
(e) Compute μX and
(f) Compute μY and
(g) Compute Cov(X,Y).
(h) Determine ρ, the correlation coefficient.
(i) Find the bestfitting line and draw it on your figure.
Answer
Step 1 of 14</p>
Here we are finding the value of c for that we need to arrange the values in the table
The given joint pmf is given by
x=0,1,2,3 y=0,1,2 with y
By using the given pmf form a table
Y 
0 
1 
2 
3 

0 
12c 
18c 
18c 
12c 
60c 
1 
0 
24c 
24cc 
16c 
64c 
2 
0 
0 
18c 
12c 
30c 
12c 
42c 
60c 
40c 
154c 
Step 2 of 14</p>
a) Since the total probability is one
154c=1
c=1/154
Step 3 of 14</p>
b) Substitute the c value in the above table
Y 
0 
1 
2 
3 

0 
12/154 
18/154 
18/154 
12/154 
60/154 
1 
0 
24/154 
24/154 
16/154 
64/154 
2 
0 
0 
18/154 
12/154 
30/154 
12/154 
42/154 
60/154 
40/154 
154/154=1 