Consider the following function. Given an array A$[1..$n$]$ of numbers and an input integer m m n$),$ return the sum: A$[1]+...+$ A$[$m$].$

F$($A$,$ n$,$ m$)//$ Add A$[1]$ to A$[$m$]\{$

sum $=0$;

for i $=1$ to m $\{$

sum $=$ sum $+$ A$[$i$]$;

$\}$

return sum;

$\}$

a$)$ What values of m will be the $($a$)$ worst case; $($b$)$ best case? And how many statements will be executed in these two cases?

b$)$ Based on the following probabilities, calculate the average number of statements to be executed in the average case. The probabilities that the value of m will be: Prob$($m $=1)=1/2,$ Prob$($m $=$ n$)=1/3,$ Prob$($m $=$ other values, i$.$e$.,2$ or $3$ or $...$ or n$-1)=1/[6($n$-2)].$