Hello, I would really appreciate if someone could help me out with this question.
I believe this is a Poisson Distribution because many of the properties are satisfied with this data. There is no possibility of it being Normal distribution and it cant be even be Binomial Distribution because that is only used when there are only two outcomes which is not the case here.
The problem is that how can I find out Lambda i.e. mean to prove my suggestion is appropriate?
Is it really Poisson or am I missing anything to find out the mean value.
Thank you in advance. :)
You are right in thinking that the underlying process is Poisson. To find an estimate for $\lambda$ you should use the sample mean $\bar{x}$. To find $\bar{x}$ in this case take the sum of the number of particles times the number of observations. $(0\cdot 34) + (1\cdot 46) + (2\cdot 38) + (3\cdot 19) + (4\cdot 4) + (5\cdot 2) + (6\cdot 0)=205$. Now we just divide by the total number of observations, $34+46+38+19+4+2=143$, so we get $\frac{205}{143}$ as an estimate for $\lambda$