Question: It is said that a random variable X has an increasing failure rate if the failure rate h(x) defined in Exercise 18 is an increasing

It is said that a random variable X has an increasing failure rate if the failure rate h(x) defined in Exercise 18 is an increasing function of x for x > 0, and it is said that X has a decreasing failure rate if h(x) is a decreasing function of x for x > 0. Suppose that X has the Weibull with parameters a and b, as defined in Exercise 19. Show that X has an increasing failure rate if b > 1, and X has a decreasing failure rate if b < 1.

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