Recall that a cdf F is deﬁned via F(a) = Pr[X ≤ a].
(a) In the discrete case, show that the cdf F of a random variable X contains exactly the same information as the function deﬁned via G(a) = Pr[X = a], by expressing F in terms of G and expressing G in terms of F.
(b) Compute and plot the cdf for (i) X ∼ Geom(p), (ii) X ∼ Exp(λ ).
(c) Identify two key properties that a cdf of any r.v. has to satisfy.