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stat2303_tutorial09

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Unformatted text preview: mester 1, 2010­11 STAT2303/2803 Probability Modelling/Stochastic Models be a continuous random variable with a survival function 1 , where is the cumulative distribution function of . Suppose is a hazard rate function, a) Show that 2) Let 1 log 1 b) Let and be independent continuous non-negative random variables with hazard rate functions and , respectively. Show that has a hazard , rate function of min , , log log log log c) Show that . is non-decreasing if the probability density function . follows a gamma distribution with parameters and with respect to the arguments, i.e. for when 1 , Γ / Γ Γ 1 Since 1 decreasing with 0 put is a non-increasing function of Page 2 of 5 when 1, is non- Semester 1, 2010­11 STAT2303/2803 Probability Modelling/Stochastic Models 3) Let , 0 be a Poisson process with rate , and be a random variable independent of and exponentially distributed with parameter . Calculate , where 0 is a constant...
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