Q82 / 160 · TS EAMCET 2021 (04 Aug Shift 2) · Mathematics

If ' $m$ ' is the mean of a Poisson distribution, then $P (x > 0) =$

Solution

If ' $m$ ' is the mean of a Poisson distribution, then

$P (x = k)$ $= \frac{m^{k} . e^{- m}}{k!}$

Now, $P (x > 0) = 1 - P (x = 0)$

$\Rightarrow P (x > 0) = 1 - \frac{m^{x} . e^{- m}}{x!}$

$= \frac{1 - \frac{1}{e^{m}}}{1}$

$= \frac{e^{m} - 1}{e^{m}}$

Hence, the correct answer is option: 'C'.