Let X be a non-negative continuous random variable with density function f(t) and distribution function F(t). The failure rate (or hazard rate) function is defined by r(t) = f(t) / (1 - F(t)). If we think of the random variable in question as being the length of a component, r(t) is proportional to the probability of failure in a small interval of time t, given that the component has survived up to time t. Show that (a) for an exponential density function, r(t) is constant. (b) for a Weibull density function with m > 1, r(t) is an increasing function of t.