7. Correct. The answer is true
a) The marginal probability function for U is given by P(U=u) = f1(u) and can be obtained from the margin totals in the right right-hand column of the following table:
U,V |
0 |
1 |
2 |
3 |
Totals |
0 |
0 |
b |
2b |
3b |
6b |
1 |
2b |
3b |
4b |
5b |
14b |
2 |
4b |
5b |
6b |
7b |
22b |
Totals |
6b |
9b |
12b |
15b |
42b |
P(U=u) = f1(u):
P(U=0) = 6b=1/7
P(U=1) = 14b=1/3
P(U=2) = 22b = 11/21.
Remember b = 1/42. Check that: 1/7 + 1/3 + 11/21 = 1
b) The marginal probability function for V is given by P(V=v) = f2(v) and can be obtained from the margin totals in the last row column of the table above:
P(V=v) = f2(v):
P(V=0)= 6b=1/7
P(V=1)=9b=3/14
P(V=2)=12b=2/7
P(V=3)=15b=5/14.
Remember b = 1/42. Check that: 1/7 + 3/14 + 2/7 + 5/14 = 1