If we let X = The number of events in a given interval,
Then, if the mean number of events per interval is
The probability of observing x events in a given interval is given by
Poisson Distribution function $P\left ( X=x \right ) =\frac{e^{-\lambda }\lambda ^{x}}{x!}$
Given Distribution function $f\left ( x \right )=\frac{e^{-2 }2 ^{x}}{x!}$
Comparing both the function
SO Mean $\left ( \lambda \right )=2$