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Poisson Process Arrival Rate Estimation enter image description here

I think we are supposed to use the fact that Poisson is memoryless but I don't understand how that helps us in calculating the arrival rate.

TShiong
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    Likely you are intended to apply a max likelihood estimate of $\lambda$ given $X_1=2,X_2=12,X_3\geq 7$. – Michael Dec 03 '22 at 21:54
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    @Michael where to be clear, $X_i$ is the $i^{\rm th}$ interarrival time and not a counting random variable. – heropup Dec 03 '22 at 21:55
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