Question #123910

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)

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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