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

We have,

X ~ Poisson($\lambda$), $\lambda$ > 0

For Poisson distribution mean = $\lambda$, then by the problem we have $\lambda$ = 0.4.

The p.m.f. of X is given by,

P(X = x) = $\begin{cases} \frac{e^{-0.4}.(0.4)^x}{x!} &\text{if } x=0,1,2,...\infty \\ 0 &otherwise \end{cases}$

The probability that the random variable is greater than 0

= P(X > 0)

= 1 - P(X = 0) [since the total probability is 1]

= 1 - $\frac{e^{-0.4}.(0.4)^0}{0!}$

= 1 - 0.6703 = 0.3297 (rounded to 4 decimal places)

Answer: The probability that the random variable is greater than zero is 0.3297.