Interarrival time

TorioSeduto

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Nov 13, 2021
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Given a time period of 122 days. It was observed that a cat crossed a road 11 times. It is announced that the number of days elapsed between one crossing and the next was as follows:

4 Days, 1 Day, 9 Days, 14 Days, 1 Day, 11 Days, 3 Days, 7 Days, 15 Days, 18 Days.

Currently, 39 days have passed since the last recorded crossing without this crossing.

Is it possible to calculate in how many days it will be most likely that the cat will cross the street again?



I know that the Poisson distribution should be used for this kind of problem

[math]P(x) \,=\, \frac{\lambda^{x}}{x!} \cdot e^{-\lambda}[/math]
 
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