You are watching an arrival process in continuous time. You are required to say the word now immediately after the arrival event that you think to be the last one to occur before a particular time t >0. You win if you succeed; otherwise you lose. If no
arrival event occur before time t , you lose. Similarly, if you fail to say `now' before time t, you lose. You may assume that the expected number of arrivals by t is greater than one.
Consider the strategy in which you pick a threshold time s element (0,t) and say `now' immediately after the the fi rst arrival that occurs after s
(a) Calculate an expression for the probability that you win using this strategy
(b) Which value of s maximizes the probability of winning? What is the corresponding optimal probability of winning?
What approach should i be looking at? I seem to need a poisson process but cant relate it to whats being asked.
arrival event occur before time t , you lose. Similarly, if you fail to say `now' before time t, you lose. You may assume that the expected number of arrivals by t is greater than one.
Consider the strategy in which you pick a threshold time s element (0,t) and say `now' immediately after the the fi rst arrival that occurs after s
(a) Calculate an expression for the probability that you win using this strategy
(b) Which value of s maximizes the probability of winning? What is the corresponding optimal probability of winning?
What approach should i be looking at? I seem to need a poisson process but cant relate it to whats being asked.