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Maybe_Memorie

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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?