Consider the following partial ordering between randomvariables X

_{1}and X

_{2}. The randomvariable X

_{1}is said to be smaller than the random variable X

_{2}in the completion rate sense if the completion rate of X

_{1}at time t, say λ1(t), is larger than or equal to the completion rate of X

_{2}, say λ

_{2}(t), for any t.

(a) Show that this ordering is equivalent to the ratio (1−F_{1}(t))/(1−F_{2}(t)) being monotone decreasing in t. (b) Show that

monotone likelihood ratio ordering ⇒ completion rate ordering ⇒ stochastic ordering.