3. Suppose that h(x) is the hazard function of X, and h(x)=\ for all x. (a) Calculate the survival function S(x). (b) Derive the mean life E(X) and the mean residual life E(X-x|X>x), where E(X) is a special case of mean residual life with x=0. (c) Based on your answer in (b), do you think h(x) can be used to model human lifespan?
3. Suppose that h(x) is the hazard function of X, and h(x)=\ for all x. (a) Calculate the survival function S(x). (b) Derive the mean life E(X) and the mean residual life E(X-x|X>x), where E(X) is a special case of mean residual life with x=0. (c) Based on your answer in (b), do you think h(x) can be used to model human lifespan?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Step 1: Survival function S(x)
To calculate the survival function S(x) when the hazard function h(x) is constant (i.e.,
Since
Now, we can plug this result into the survival function formula:
a) So, the survival function S(x) is exp(-λx).
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