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.
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.
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.
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.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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