= Solution
For <fractional event imputation>, let $q_j$ be the fractional event weight assigned to the seventh individual at $t_j$. Its event contribution at $t_j$ is $q_j$. It belongs to the <risk set> at that time precisely for allocations at $t_j$ or later, so its fractional <risk set> contribution is $\sum_{j'\ge j}q_{j'}$. This justifies both parts of the hint.
For $(q_4,q_5,q_6)=(1/2,1/4,1/4)$, the fractional counts at the last three times are
$$
(r_4,d_4)=(4,3/2),\qquad(r_5,d_5)=(5/2,5/4),\qquad(r_6,d_6)=(5/4,5/4).
$$
Earlier <Kaplan–Meier estimator> factors still give survival $4/7$ immediately before $t_4$. Consequently
$$
\boxed{\widehat F_5^1=\frac47\left(1-\frac{3/2}{4}\right)\left(1-\frac{5/4}{5/2}\right)=\frac5{28}.}
$$
\b[The three values are] $\widehat F_5^0=1/7\simeq0.1429$, $\widehat F_5^1=5/28\simeq0.1786$, and $\widehat F_5^*=4/21\simeq0.1905$, in strictly increasing order. Spreading the censored individual's mass beyond $t_4$ raises the survivor estimate from the immediate-event imputation and moves it toward the original <Kaplan–Meier estimator>.
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