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Homework Statement
Homework Statement
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 anyone 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 anyone day one or more type B are detected, what is the probability one or more type A are also detected?
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?