Suppose we refer to the MDP defined above as M$1,$ and write V$$

M$1$

$($s$1),$V$$

M$1$

$($s$2)$ to

represent the optimal values the M$1.$ Now define another MDP M$2$ that is exactly the same as M$1$ except

that the rewards are now RM$2$

$($s$1)=2$ and RM$2$

$($s$2)=4.$ Namely, M$2$ differs from M$1$ only in that the

reward on each state is twice as large. We write the optimal values of M$2$ as V $$

M$2$

$($s$1)$ and V $$

M$2$

$($s$2).$

Now, suppose you know what V$$

M$1$

$($s$1)$ and V$$

M$1$

$($s$2)$ are $($which you don$$t$,$ and you do not need to

implement it to find out$),$ then what should V$$

M$2$

$($s$1)$ and V$$

M$2$

$($s$2)$ be$?$ That is$,$ write down the values of

V$$

M$2$

$($s$1)$ and V $$

M$2$

$($s$2)$ using the values of V $$

M$1$

$($s$1)$ and V $$

M$1$

$($s$2).$ Explain your reasoning