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Suppose that we have a Calling Center in which a random caller (discrete random variable) Xd with (generalized) PDF and CDF fd(x) and Fd(x), and a continuous random variable Xc with PDF and CDF fc(x) and Fc(x). Now we create a new Calling System with random variable X in the following way. We have a caller with P(H)=p. if a call connects, then the value of X is determined according to the probability distribution of Xd. If the call does not connects, the value of X is determined according to the probability distribution of Xc a. Find the CDF of X, F(x). b. Find the PDF of X, f(x). c. Find E(X). & Var(X)
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