The charge e on one electron is too small to measure. However, one can make measurements of the current I passing through a detector. If N is the number of electrons passing through the detector in one second then I=eN. Assume N is Poisson. Show that the charge on one electron is given by Var(I)/E[I].

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The charge e on one electron is too small to measure. However, one can make measurements of the current I passing through a detector. If N is the number of electrons passing through the detector in one second then I=eN. Assume N is Poisson. Show that the charge on one electron is given by Var(I)/E[I]. 

Expert Solution
Step 1: Given information.

The charge on one electron is e.

The total number of electrons passing through the detector is N.

The total current passing through the detector is I and it is given as I equals e N.

Also, N follows the Poisson distribution.

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