Answer to Question #119382 in Statistics and Probability for Michael

Question

A random variable X has Poisson distribution with mean equal to 0.4. What is the
probability that the random variable is greater than zero?

Answer 1

The aim is to compute $P(X>0)$. We remind that for the Poisson distribution with the mean equal to $0.4$ we have

$P(X=k)= \frac{(0.4)^{k}}{k!}e^{-0.4}.$

Thus, using the Taylor series for the exponent, we have

$P(X>0)=\sum_{k=1}^{+\infty} \frac{(0.4)^{k}}{k!}e^{-0.4}=e^{-0.4}(e^{0.4}-1)=0.3297$