$(15$ points$)$ Consider the $k-$arm bandit problem. If the step$-$size parameters, ${}_n,$ are not

constant, then the estimate $Q_n$ is a weighted average of previously received rewards. What

is the weighting on each prior reward $R_k,1kn$ for the general case in terms of the

sequence of step$-$size parameters ${}_1,{}_2,{}_3$dots,${}_n?$