Probability of a successful photo

Reference no: EM13985426

Peter wishes to take a picture of his girlfriend Sheila. Since they are in a rather dark room, he needs a rather long exposure time, during which Sheila must not move. The following model can be used to describe the situation. The success of a photo is called an "A-event." Each time Sheila moves, she causes a disturbance called a "D-event." A-events and D- events occur according to independent Poisson processes with intensities λA and λD , respectively. The experiment is started at time t = 0. Let T be the time of the first A-occurrence. 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?

Reference no: EM13985426

Questions Cloud

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.

Determine the amount available for distribution : Determine the amount available for distribution to all claimants.

User Account

All Pages