**7. Correct. The answer is true**

a) The marginal probability
function for U is given by P(U=u) = f_{1}(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) = f_{1}(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) = f_{2}(v) and can be obtained from
the margin totals in the last row column of the table above:

P(V=v) = f_{2}(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