BLOSUM $[10$ points$]$

Consider the following four blocks on the alphabet $=\{A,T,C,G\}.$

Using $L=0,$ such that the above four blocks are not pruned down, compute the

BLOSUM$0$ scoring matrix. Use $=0\mathrm{.}5,$ the natural logarithm and round up to the

nearest integer $($i$.$e$.$ take the ceiling$).($i$)$ Give $q_x$ and $($ii$)p_{x,y}$ for each $x,$yin$.$

Clearly indicate the denominator used for computing these two quantities.