Let x > 0 be a lifetime with survival function s(x). Let x > 0, t...

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Let x > 0 be a lifetime with survival function s(x). Let x > 0, t > 0 be two times. Suppose that P(X > x) > 0. Show that: a) P(x<x< x+t |X>a)= S(x)-S(a+t) S(x) b) P(X>x+t] X>a) = S(a+t) Let x > 0 be a lifetime with survival function s(x). Let x > 0, t > 0 be two times. Suppose that P(X > x) > 0. Show that: a) P(x<x< x+t |X>a)= S(x)-S(a+t) S(x) b) P(X>x+t] X>a) = S(a+t)