Can you prove that the shortest job first scheduling algorithm is optimal in that it minimizes the average waiting time. For simplicity, assume that $1)$ all n process are already in the system at the time the scheduling decision has to be made and $2)$ all processes have arrived at the same time.

mathcal T n $+1=(1-$ alpha$)^$ n$+1$ tau $0+$ alpha sum k$=0^$ n $(1-$ alpha$)^$ n$-$k t k