Finding X for density functionA city's fire brigade is deployed approximately every 2 days to...





Finding X for density function
A city's fire brigade is deployed approximately every 2 days to extinguish a fire. The number of operations X per week is assumed to be Poisson distributed. Calculate the density and the distribution function of the time T that elapses between two fires. Represent both functions graphically.
I have this formula for the density function:
f ( x ) = μ x x ! exp μ
μ = 2 because 2 days pass between fires I think but I am not sure what X should be.

Answer & Explanation

Patricia Curry

Patricia Curry


2022-06-25Added 15 answers

Step 1
If the model il poisson with a mean of 2 days, this means that T, the interarrival time between two fires, is exponentially distributed with mean 1/2 days, say f T ( t ) = 2 e 2 t   [ t > 0 ] the proof is very simple. Understood this, the rest is immediate

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