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

$$P(X=x)={e^{-\mu}\cdot \mu^x \over x!}$$

Given $\mu=0.4$

$$P(X=0)={e^{-0.4}\cdot 0.4^0 \over 0!}=e^{-0.4}$$

$$P(X>0)=1-P(X=0)=1-e^{-0.4}\approx0.330$$