Question: Let X be a r.v. with d.f. F; i.e., F(x) = P(X ( x), x ( (. Then show that (i) P(X < x) =

Let X be a r.v. with d.f. F; i.e., F(x) = P(X ( x), x ( (. Then show that
(i) P(X < x) = F(x -) (the left-hand side limit).
(ii) F(x) is continuous at x if and only if P(X = x) = 0.

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