ISRO2009-66

Question

If the pdf of a Poisson distribution is given by $f(x) = \dfrac{e^{-2} 2^x}{x!}$ then its mean is

• A. $2^x$
• B. $2$
• C. $-2$
• D. $1$

Answer 1

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 $\left ( \lambda \right )=2$