$($d$)$ If stock $2$ has a three$-$for$-$one stock split at open, that is$,$ each of the shares you own becomes three shares, with the price being a third $(20$ at open, $18$ at close in this case$).$ What will the new

weighing denominator for the price$-$weighted index be$?$ What will be the close price for the price$-$

weighted index?

$($e$)$ If stock $4$ has a two$-$for$-$one stock split at open, that is$,$ each of the shares you own becomes two

shares, with the price being half $(103$ at open, $98$ at close in this case$).$ What will be the close

price for the value$-$weighted index?