QUESTION TWO (20 MARKS) Consider a discrete random variable taking values 0, 1, 2, 3,... Find...

 

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QUESTION TWO (20 MARKS) Consider a discrete random variable taking values 0, 1, 2, 3,…... Find E(T) as a function of the survivor function. Hence find the mean of the random variable whose survivor function is given as follows. [5 marks] (a) t F(t) (b) 0 1 1 0.8 2 0.6 3 0.4 Suppose the failure time T has a Weibull distribution with pdf f(t) = Ba(at)B-1 ext(-(at) ³) t ≥ 0 (i) Derive the survivor and hazard functions (ii) Derive the mean of T 4 0.2 5 0.1 [10 marks] [5 marks] QUESTION TWO (20 MARKS) Consider a discrete random variable taking values 0, 1, 2, 3,…... Find E(T) as a function of the survivor function. Hence find the mean of the random variable whose survivor function is given as follows. [5 marks] (a) t F(t) (b) 0 1 1 0.8 2 0.6 3 0.4 Suppose the failure time T has a Weibull distribution with pdf f(t) = Ba(at)B-1 ext(-(at) ³) t ≥ 0 (i) Derive the survivor and hazard functions (ii) Derive the mean of T 4 0.2 5 0.1 [10 marks] [5 marks]

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Lets go through each part and provide the correct answers a To find ET as a functi... View the full answer