6 Nuts and raisins occur in randomly chosen squares of a particular brand of chocolate. The numbers of nuts and raisins are denoted by \(N\) and \(R\) respectively and the joint probability distribution of \(N\) and \(R\) is given by $$f ( n , r ) = \begin{cases} c ( n + 2 r ) & n = 0,1,2 \text { and } r = 0,1,2
0 & \text { otherwise } \end{cases}$$ where \(c\) is a constant.

1. Find the value of \(c\).
2. Find the probability that there is exactly one nut in a randomly chosen square.
3. Find the probability that the total number of nuts and raisins in a randomly chosen square is more than 2 .
4. For squares in which there are 2 raisins, find the mean number of nuts.
5. Determine whether \(N\) and \(R\) are independent.