Consider a DataFrame df$.$ We want to create groups based on the column group$\_$key in the DataFrame and fill the nan values with group means using:

$1$ filling$\_$mean $=$ lambda $g$:$g*fillna(g*mean())$

Which of the following is correct for performing this task?

df$.$groupby$($group$\_$key$).$apply$($filling$\_$mean$)$

df$.$groupby$($group$\_$key$).$filling$\_$mean$()$

df$.$groupby$($group$\_$key$).$transform$($filling$\_$mean$)$

df$.$groupby$($group$\_$key$).$aggregate$($filling$\_$mean$)$