Homework 3 . Due Sept. 28, 2016 


(1). If X has hazard h1(t); Y has hazard h2(t) and X, Y are independent. Show that min(X, Y) has hazard  h1(t) + h2(t).
     What is the survival function of min(X, Y) ?

(2). We have defined the Kaplan-Meier estimator

    1- \hat F_{KM} (t) = \prod_{ s<= t}  [ 1 - dN(s)/ R(s) ] . 


    Now suppose there is no censoring before time T (i.e. all censoring ocure after T)
    Simplyfy the Kaplan-Meier estimator 1- \hat F_{KM}(T) to 
     #{ T_i > T} / n  where n is the sample size.




3. For the "myel" data in our textbook, compute the Kaplan-Meier estimator, Altshuler estimator and 
   the Nelson Aalen estimator.


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