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Chinnu
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Homework Statement
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 (t1) to go from A to B is Poisson and is given by Pab(t1) and the for B to C is t2 and the distribution is Pbc(t2). You are given:
Pab(t1) = k1exp(-k1t1) and Pbc(t2) = k2exp(-k2t1)
So the total time to go from A to C is t = t1 + t2
Derive the distribution of t, that is, find Pac(t). Also find the mean of this distribution in terms of k1 and k2.
Homework Equations
We can use the basic rules of probability,
The Attempt at a Solution
Is it as simple as this?:
Pac(t) = k1Pab(t1) + k2Pbc(t2)
or is it:
Pac(t) = k1k2exp(-k1t1-k2t2)
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