A Geiger counter beeps according to a Poisson arrival process, with rate 1 beep per minute. A Geiger counter beeps according to a Poisson arrival process, with rate 1 beep per minute. Let T_3 be the time in minutes from when the Geiger counter is turned on until the third beep. Find P( 1 < T_3 < 3 ) = probability T_3 falls in interval (1,3). Can someone check which of my answers are correct? ![enter image description here]( ![enter image description here](

Yes, if you seek the probability that the third beep occurs after one minute but not after three minutes, then your first method is correct. $$\mathsf P(1< T_3\leqslant 3)~{=\mathsf P(1