1. The problem statement, all variables and given/known data 1. The problem statement, all variables and given/known data A particle detector is set up to detect type A particles. These are detected as a poisson process with parameter lamda = 0.5 per day. (i) What is the probability that 3 or more will be detected in any one day? (ii) What is the distribution of inter-detection times for these particles? (iii) What is the probability that the inter-detection time for two consecutive particles will be less than 3 days? (iv) The detector also detects type B particles. These occur with rate lamda = 0.5 when no type A are detected, and rate lamda = 1 when 1 or more type A are detected. If on any one day one or more type B are detected, what is the probability one or more type A are also detected? 3. The attempt at a solution (i) was easy. I got 0.01439 For (ii) I have absolutely no idea what to do. For (iv), I used P(at least 1 A | at least 1 B) = (at least 1 A and 1 B)/P(at least 1 B) I ended up getting 0.2425. Is this correct?