Question: Problem 6.24: If the random variable T is the time of failure of a commercial product and the values of its probability density and distribution function at time t are \(f(t)\) and \(F(t)\), then its failure rate is given by

\[\frac{f(t)}{1-F(t)}\]

(a) Show that if T has an exponential distribution, the failure rate is constant.

(b) If T has a Weibull distribution prove

\[\frac{f(t)}{1-F(t)}={{\beta }^{k}}k{{t}^{k-1}}\]