Cars arrive at a small gas station to refuel according to a Poisson process with rate 30 per hour, and have an exponential service time distribution with mean 4 minutes. Since there are four gas pumps available…

Question: Cars arrive at a small gas station to refuel according to a Poisson process with rate 30 per hour, and have an exponential service time distribution with mean 4 minutes. Since there are four gas pumps available, four cars can refuel simultaneously, but unfortunately there is no room for Read more…

Let X1, … , Xn be non-negative independent random variables with continuous distributions (but X1, … , XN are not necessarily identically distributed)…

Question: Let X1, … , Xn be non-negative independent random variables with continuous distributions (but X1, … , XN are not necessarily identically distributed). Assume that the PDFs of Xi’s are uniformly bounded by 1. (a) Show that for every i, Eſexp(-tX;)] = Į, for all t > 0. (b) Read more…