Understanding what x~pois(6) means

Question

After a brief checkout on poisson distribution i understand that poisson has results in outomes that can be described as success or failures

And also that poisson probability is found by

P(x; μ) = (e-μ) (μx) / x!

What am not getting is how to interprete this

X ∼ POIS(6)

A small thought would be that x iis normally distributed as a posson of 6 or how do i go about it since am later suposed find the probability of x=0

But i would like to understand what X ∼ POIS(6) means

Answer 1

David Mitra answered your question correctly in the comments.

In general $X \sim Dist(a,b,c,...)$ means X is a random variable whose distribution is "Dist" with parameters a,b,c,...

In this case the Poisson distribution only has one parameter, $\mu$, which is equal to 6.

Answer 2

This is just a notation often used in Statistics that means $X$ has Poisson distribution, and the parameter ($\mu$) of this distribution is 6. If $X$ had Normal distribution with $\mu=10$ and $\sigma=1$, you would represent this by $$X\sim \text{Normal}(10,1)\quad \text{or} \quad X\sim \text{N} (10,1)$$ POIS is just a "nickname" used to indicate the Poisson distribution.