Suppose the fraction of a cohort of aids patients that survives a time t after aids diagnosis is given by S(t) = exp(-kt). show that the average survival time Taver after aids diagnosis for a member of this cohort is given by Taver= 1/k. show every steps for getting Taver = 1/k

Answer 1

note that

∫[0,∞] e^-kx
= -1/k e^-kx [0,∞]
= 1/k