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

Answer:

The mean and of the Needlemen-Wunch score is 13

Step-by-step 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