Suppose you are a data analyst dedicated to studying the arrival of orders in a food delivery application. Historical data suggest that order arrival can be modeled as a Poisson process with rate λ orders/minute. Furthermore, orders remain in the system for a random time of K, which follows a probability density distribution g(k). Let u(t) be the number of available delivery people at a time t, we will say that the system is congested if at a time t there are more orders than available delivery people. a.)If we know that an order has been placed between 0 and t, what is the probability that the order is in the system at t? b.)If n orders have been placed between 0 and t, what is the probability that u of them are in the system at t? c.)If we do not have information about the number of orders placed between 0 and t, what is the probability that at t the system is congested?
Suppose you are a data analyst dedicated to studying the arrival of orders in a food delivery application. Historical data suggest that order arrival can be modeled as a Poisson process with rate λ orders/minute. Furthermore, orders remain in the system for a random time of K, which follows a
a.)If we know that an order has been placed between 0 and t, what is the probability that the order is in the system at t?
b.)If n orders have been placed between 0 and t, what is the probability that u of them are in the system at t?
c.)If we do not have information about the number of orders placed between 0 and t, what is the probability that at t the system is congested?
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