I just started taking survival analysis class and I'm stumped on this question.

Let $T_{1},T_{2},...T_{n}$ independent continuous non-negative random variables with survival function $S(t)$

Show that $S(t)$ ~ $U(0, 1)$.

Find the distribution of $-log S(t)$


They meant: show that S(T_i) ~ U([0,1]). This is a consequence of the fact that if random variable X has distribution function F(x) then F(X) ~ U([0,1]).


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