Define a function MetricEntropy $($w$,$ alphabetSize$)$ that computes the metric entropy of $w$ if it is assumed that the alphabet has size alphabetSize $($that is $|A|=$ alphabetSize$).$ You must code this function for yourself and cannot use a built$-$in "Entropy" function.

Use MatLab

Definition $2\mathrm{.}1$ For $A=\{a_1,a_2,$dots,$a_n\}$ and $P_{a_i}$ the probability of occurrence in $win{A}^{**}$ of $a_i,$ then metric entropy of $w$ is given by

$H(w)=-{\displaystyle \underset{i=1}{\overset{n}{}}}{P}_{a_i}log(P_{a_i})$

For example, if $w=$ AAAACCCGGT, then $|w|=10,P_A=\frac{4}{10},P_C=$

$\frac{3}{10},P_G=\frac{2}{10},$ and $P_T=\frac{1}{10}.$ So then

$H(w)=-(\frac{4}{10}log(\frac{4}{10})+\frac{3}{10}log(\frac{3}{10})+\frac{2}{10}log(\frac{2}{10})+\frac{1}{10}log(\frac{1}{10}))=1\mathrm{.}27985$