(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Imagine you want to go from A to C via B. So you have two steps: A to B and B to C. Let's assume the time taken (t_{1}) to go from A to B is Poisson and is given by P_{ab}(t_{1}) and the for B to C is t_{2}and the distribution is P_{bc}(t_{2}). You are given:

P_{ab}(t_{1}) = k_{1}exp(-k_{1}t_{1}) and P_{bc}(t_{1}) = k_{2}exp(-k_{2}t_{2})

2So the total time to go from A to C is t = t_{1}+ t_{2}

Derive the distribution of t, that is, find P_{ac}(t). Also find the mean of this distribution in terms of k_{1}and k_{2}.

2. Relevant equations

We can use the basic rules of probability

3. The attempt at a solution

Is the distribution as simple as this?:

P_{ac}(t) = k_{1}P_{ab}(t_{1}) + k_{2}P_{bc}(t_{2})

or is it:

P_{ac}(t) = k_{1}k_{2}exp(-k_{1}t_{1}-k_{2}t_{2})

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# Homework Help: Poisson processes in series

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