15 3 Let fX1 X2 g be a sequence of independent and identically distributed random variables with PDF fXx, and let N be an integer valued random variable with PMF pNn, where N and the Xi are independent Consider a process in which events occur at times X1 X1 1 X2 X1 1 X2 1 1 XN a Calculate the mean,...

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15.3 Let fX1; X2; ...g be a sequence of independent and identically distributed random variables with PDF

Question:

15.3 Let fX1; X2; ...g be a sequence of independent and identically distributed random variables with PDF fXðxÞ, and let N be an integer-valued random variable with PMF pNðnÞ, where N and the Xi are independent. Consider a process in which events occur at times X1; X1 1 X2; ...; X1 1 X2 1?1 XN.

a. Calculate the mean, variance, and s-transform of the PDF of the time of the last event.

b. What is the expected number of events in the interval (0,t)?

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