e$.(4$ pts$)$ The profile matrix from part $($d$)$ can be represented with motif logos$.$ Show the

calculated bits for the first position in the sequence logo$.$

Note: the formula to find the information content in bits are given below.

Shannon Entropy: $H(i)=-{\displaystyle \underset{\text{b}\text{i}\text{n}\{A)}{\overset{?}{}}},C,G,T{p}_{b,i}*lo{g}_2{p}_{b,i}$

Corrected entropy: $,H^{\text{'}}(i)=\frac{b-1}{2ln(2)*N}*H(i)$

Information content: $R(i)=2\mathrm{.}0-H^{\text{'}}(i)$

where $N$ is the number of sequences, $p_{b,i}$ is the probability of nucleotide $b$ at position

i$.$