Find the distribution, Find the distribution of Tn, and

Find the distribution

Reference no: EM13985427

People arrive at an automatic teller machine (ATM) according to a Poisson process with intensity λ. The service time required at the ATM is constant, a seconds. Unfortunately, this machine does not allow for any waiting customers (i.e., no queue is allowed), which means that persons who arrive while the ATM is busy have to leave. When the a seconds of a customer have elapsed, the ATM is free to serve again, and so on. Suppose that the ATM is free at time zero, and let Tn be the time of the arrival of the nth customer. Find the distribution of Tn, and compute E Tn and Var Tn. Remark. Customers arriving (and leaving) while the ATM is busy thus do not affect the service time.

Reference no: EM13985427

Questions Cloud

Compute the expected value of the total amplitude : We finally assume that the initial amplitudes of the pulses are independent of the Poisson process. Compute the expected value of the total amplitude at time t.

Explain why such a small figure is plausible : Studies have concluded that the dead weight loss of monopoly power in the United States is less than 0.5 percent of GNP. From your knowledge of the determinants of the dead-weight loss, explain why such a small figure is plausible.

Compute the expected value of the total waiting time : Compute the expected value of the total waiting time of all passengers who have come to the station in order to catch a train that leaves at time t.

What two quantities are conserved throughout the motion : Draw a diagram showing the direction of the incoming puck, the orientation of the string, and the direction of motion of the puck on the string after the elastic collision.

Find the distribution : Find the distribution of Tn, and compute E Tn and Var Tn. Remark. Customers arriving (and leaving) while the ATM is busy thus do not affect the service time.

Probability of a successful photo : The experiment is deemed successful if T ≥ 1 and if no D-event occurs during the time interval (0, T + 2]. What is the probability of a successful photo?

Determine the acceleration of the bullet : A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The bullet penetrates for a distance of 0.0621 m before it comes to stop. Determine the acceleration of the bullet while moving into the clay. (Assume a uniform accele..

Poisson process with intensity : A radio amateur wishes to transmit a message. The frequency on which she sends the Morse signals is subject to random disturbances according to a Poisson process with intensity λ per second.

Discuss how you may have used tvm in a recent investment : Discuss how you may have used TVM in a recent investment or loan decision and explain some of the TVM details that may have been involved in your transaction.

User Account

All Pages