Villaretq0

2022-06-24

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:
$f\left(x\right)=\frac{{\mu }^{x}}{x!}\cdot {\mathrm{exp}}^{-\mu }$
$\mu =2$ because 2 days pass between fires I think but I am not sure what X should be.

Patricia Curry

Expert

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 the proof is very simple. Understood this, the rest is immediate

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