1.9.3 Show that, for an exponential survival distribution, the probability of surviving past time t +...

 

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1.9.3 Show that, for an exponential survival distribution, the probability of surviving past time t + t₁ given that an individual has survived past to equals the unconditional probability of surviving past t₁. In other words, the probability of surviving t, more units of time is the same at the beginning as it is after surviving to units of time. This is often referred to as the "memoryless" property of the exponential distribution. Hint: In symbols, this means that S(t + t,)/S(t) = S(t₂). 1.9.3 Show that, for an exponential survival distribution, the probability of surviving past time t + t₁ given that an individual has survived past to equals the unconditional probability of surviving past t₁. In other words, the probability of surviving t, more units of time is the same at the beginning as it is after surviving to units of time. This is often referred to as the "memoryless" property of the exponential distribution. Hint: In symbols, this means that S(t + t,)/S(t) = S(t₂).

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