Let T be a random variable with PDF f(t) and CDF F(t).
The hazard function of T is defined by
h(t) = f(t) / (1 â F(t))
(a) Suppose T represents a personâs lifetime, and let t be a
positive number. Explain why h(t) is the probability density for death at
time t (that is, h(t) dt is the probability for death between time t and time
t + dt), given that the person has survived up to time t.
(b) Suppose T ⌠Expo(λ). Let t > 0. Compute h(t), and
interpret your result in terms of what you know about the exponential distribution.