A prospective study with a 2-year (24-month) follow-up was conducted among 10 residents of a nursing home in Springfield Illinois. Results are shown in the table for all individuals who either died or were censored before the end of the follow-up period.

Follow-up Time (Months)	Events
2	Death
4	Censored
7	Censored
8	Death
12	Censored
15	Death
17	Death
19	Death
20	Censored
23	Death

Using the data from the table, calculate for all deaths (fill in the table below):

1. The probability of death at the exact time when each death occurred (2 points)
2. The probability of survival beyond the time when each death occurred (2 points)
3. The cumulative probabilities of survival (2 points)

Follow-up Time (Months)	Event	Probability of death at the exact time when the death occurred	Probability of survival beyond the point when the death occurred	Cumulative probability of survival beyond the time when death occurred
2
8
15
17
19
23

IV. What is the cumulative survival probability at the end of the follow-up? (2 points)

V. What is the simple proportion of individuals apparently surviving (i.e., not observed to die) through the end of the study's observation period? (2 points)

VI. Why are the simple proportion of surviving and the cumulative probability of survival different? (5 points)