Exercise 46b, ch 5 (Show that an Exponential r.v. has a constant hazard function)

The problem

Let T be the lifetime of a certain person (how long that person lives), and let T have CDF F and PDF f. The hazard function of T is defined by

h(t) = f(t)/1 - F(t)
:
(a) Explain why h is called the hazard function and in particular, why h(t) is the
the probability density for death at time t, given that the person survived up until then.

(b) Show that an Exponential r.v. has a constant hazard function and conversely, if the
hazard function of T is a constant then T must be Expo(lambda) for some lambda.


Tags
Mathematical statistics, probability, hazard function, exponential random variable


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