6. Correct. The answer is false
Sample points and their associated probabilities are shown in 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 |
(a)Since the grand total, 42b, must equal 1, b= 1/42.
(b)From the table P(U=2, V=1)= 5b + 5/42.
(c)From the table
P(U ≥1, V≤ 2) = ∑ ∑ f(u,v)
u≥1
v≤ 2
P(U ≥1, V≤ 2)= (2b +3b + 4b) + (4b + 5b + 6b)
P(U ≥1, V≤ 2)=4/7