12. The failure rate (or hazard rate) function of a random variable X is defined by r (t ) = f (t ) , where f is the p.d.f. and F is the c.d.f. 1 - F(t (a) Show that the failure rate function for an exponential random variable is constant. (b) Show that the exponential distribution is the only continuous random variable with range {x > 0} that has a constant failure rate function. (c) Determine the failure rate function if X has a gamma distribution with parameters 2 and 2. (d) Suppose that X represents the lifetime of an electrical component and the corresponding r (t) is a decreasing function of t. Explain what this means about the component