Let X be a continuous non-negative random variable with distribution function F(x) and probability density function f(x)

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Let X Be A Continuous Non Negative Random Variable With Distribution Function F X And Probability Density Function F X 1 (119.68 KiB) Viewed 100 times

(b) Consider a certain type of organ in the human body that
degrades gradually at a slow but steady rate. To model this, we
suppose that its failure rate function is linearly increasing r(x)
= ax for some a > 0. It has been observed that the median
lifetime of the organ is 60 years. What is the probability that
such an organ lasts for more than 100 years?
Let X be a continuous non-negative random variable with distribution function F(x) and probability density function f(x) which is such that f(x) = f'(x) for all x € (0,0). Define the failure rate function (also called hazard function) as f(x) r(x) 1 – F(x)' and the survival function as G(x) = 1 – F(x). (a) Show that for a non negative continuous random variable X with failure rate function r, X has survival function C(ar) = exp(- [*r(du)