The Needleman-Wunsch method for aligning DNA sequences assigns 1 point whenever a mismatch occurs, and 3 points whenever a gap (insertion or deletion) appears in a sequence. Assume that under certain conditions, the number of mismatches has mean 5 and standard deviation 2, and the number of gaps has mean 2 and standard deviation 1.

a. Find the mean of the Needleman-Wunsch score.

b. Assume the number of gaps is independent of the number of mismatches. Find the variance of the Needleman-Wunsch score.