*22. Let X denote the lifetime of an item. Suppose the item has reached the age of t. Let denote its remaining life and define In words, is the probability that a t-year-old item survives an additional time

a. Show that

(a) where F is the distribution function of X.

(b) Another definition of IFR is to say that F is IFR if decreases in t, for all

a. Show that this definition is equivalent to the one given in the text when F has a density.