For a negative exponential survival function S(t), recall that S(t) = exp(t), where  is the rate parameter or hazard rate function. Consider the conditional probability that the survival time is T > t2, given that we know T > t1, where t1 < t2. Denote by S(t2|t1) the conditional probability of survival beyond t2, given that the patient survives beyond t1, i.e., P[T > t2|T > t1]. Show that S(t2|t1) = exp[(t2 – t1)]. The term exp[(t2 – t1)] is called the lack of memory property of the negative exponential lifetime model because the survival at time t1 has the same distribution as the survival at time 0; if = t2 – t1, the probability of surviving units of time is the same at 0 as it is at t1, namely exp(). The probability of surviving depends only on and not on the time t1 that we are conditioning on.