7. Tetrahedral dice have four faces. Two fair tetrahedral dice, one red and one blue, have faces numbered \(0,1,2\), and 3 respectively. The dice are rolled and the numbers face down on the two dice are recorded. The random variable \(R\) is the score on the red die and the random variable \(B\) is the score on the blue die.

1. Find \(\mathrm { P } ( R = 3\) and \(B = 0 )\). The random variable \(T\) is \(R\) multiplied by \(B\).
2. Complete the diagram below to represent the sample space that shows all the possible values of \(T\).
   \includegraphics[max width=\textwidth, alt={}, center]{af84d17b-5308-4b1e-99b5-40c5df5bf01e-13_732_771_834_621} \section*{Sample space diagram of \(T\)}
3. The table below represents the probability distribution of the random variable \(T\).

   \(t\)	0	1	2	3	4	6	9
   \(\mathrm { P } ( T = t )\)	\(a\)	\(b\)	\(1 / 8\)	\(1 / 8\)	\(c\)	\(1 / 8\)	\(d\)

   Find the values of \(a , b , c\) and \(d\). Find the values of
4. \(\mathrm { E } ( T )\),
5. \(\operatorname { Var } ( T )\).