Question: 6. If T is a continuous random variable that is always positive (such as a waiting time), with probability density function f (t) and cumulative

6. If T is a continuous random variable that is always positive (such as a waiting time), with probability density function f (t) and cumulative distribution function F(t), then the hazard function is defined to be the function h(t) = f (t) 1 − F(t) The hazard function is the rate of failure per unit time, expressed as a proportion of the items that have not failed.

a. If T ∼ Weibull(α, β), find h(t).

b. For what values of α is the hazard rate increasing with time? For what values of α is it decreasing?

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