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answerhappygod
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You were given the definition of hazard function (or failure rate) h(t), survivor function S(t), and density function f(t) for a failure time random variable T, find or derive (i) the relationship between S(t) and h(t), and (ii) the relationship between S(t) and the cumulative hazards function H(t), i.e. show that = ds(t)/dt h(t) -S(t) S(t) = exp{-H(t)} where H(t) = S'h(t) dt.
You were given the definition of hazard function (or failure rate) h(t), survivor function S(t), and density function f(t) for a failure time random variable T, find or derive (i) the relationship between S(t) and h(t), and (ii) the relationship between S(t) and the cumulative hazards function H(t), i.e. show that = ds(t)/dt h(t) -S(t) S(t) = exp{-H(t)} where H(t) = S'h(t) dt.