Consider Example 10.3, where we observe series-system lifetimes of a series system. We observe n different systems that are each made of k i identical components (i = 1, . . . ,n) with lifetime...

Consider Example 10.3, where we observe series-system lifetimes of a series system. We observe n different systems that are each made of k_i
identical components (i = 1, . . . ,n) with lifetime distribution F. The lifetime data is denoted (51, . . ., z,) and are possibly right censored. Show that if we let r_j
= k_j
+. . . +in, the likelihood can be expressed as (10.5) and solve for the nonparametric maximum likelihood estimator.