Probability of a successful photo

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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

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