A small prospective study is run and follows ten participants for the development of myocardial infarction (MI, or heart attack) over a period of 10 years. Participants are recruited into the study over a period of two years and are followed for up to 10 years. Below are the times, in years, to development of MI. Censored observations are denoted by a plus (+) sign.

Patient Number	Time (years)
1	10+
2	4
3	9
4	4+
5	7
6	10+
7	2
8	10+
9	10+
10	3

How many occurrences of MI were observed in this sample of patients? Use the product limit method to calculate the survival function, Ŝ(t). What is Ŝ(4), the estimated cumulative probability of not having an MI beyond 4 months? Conditional on getting to year 9 without an MI, what is the estimated probability of getting an MI during year 9? What is the estimated cumulative probability of surviving beyond year 10?

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