2. (40 points) For the following survival data with "+" indicating censored subjects::

6, 6, 6, 6+, 7, 9+, 10, 10+, 11+, 13, 16, 17+, 19+, 20+, 22, 23, 25+, 32+, 32+, 34+, 35+

(a) Produce a plot of the Kaplan Meier estimate for T, along with 95% confidence intervals using Greenwood's approximation method.

(b) Produce a plot of the Kaplan Meier estimate for T, along with 95% confidence intervals using the log-log approximation method.

(c) Produce a plot of the Kaplan Meier estimate for T, along with 95% confidence intervals using the log approximation method.

(d) Let S(t) and S(t) denote the Kaplan-Meier estimator and the Fleming- Harrington estimator of the survivorship function of the event time, respectively. Calculate S(16) and S(16) by hand. What is the standard error of S(16)?

(e) (A problem for PhD students: 10 points) What is the standard error of S(16)?

please use r as you explain