Question

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 7 and standard deviation 4, and the number of gaps has mean 2 and standard deviation 1. Find the mean and of the Needlemen-Wunch score.

Answer 1

The mean and of the Needlemen-Wunch score is 13

Explanation:

Consider the provided information.

Let X is the 1 point whenever a mismatch occurs and Y is the 3 points whenever a gap appears in a sequence.

Assume that under certain conditions, the number of mismatches has mean 7 and standard deviation 4,
`\mu_X=7\ and\ \sigma_x=4`

The number of gaps has mean 2 and standard deviation 1.
`\mu_Y=2\ and\ \sigma_Y=1`

Now use the formula :
`\mu_(c_1X_1+c_2X_2+...+c_nX_n)=c_1\mu_(X_1)+c_2\mu_(X_2)+...+c_n\mu_(X_n)`

`\mu_(X+3Y)=\mu_(X)+3\mu_(Y)`

Substitute the respective values as shown:

`\mu_(X+3Y)=7+(3)(2)`

`\mu_(X+3Y)=7+6=13`

Hence, the mean and of the Needlemen-Wunch score is 13