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...

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? c) If T has an exponential distribution, show that the hazard function is constant.