Question

problem with Poisson distribution, please help

The number of dirt specks on a randomly selected
square yard of polyethylene film of a certain type
has a Poisson distribution with a mean value of 2
specks per square yard. Consider a random sample of n=5 film specimens, each having area 1
square yard, and let X(bar) be the resulting sample
mean number of dirt specks. Obtain the first 21
probabilities in the X(bar) sampling distribution. [Hint: What does a moment generating function argument say about the distribution of X1+X2+...+X5?]

Thanks beforehand

Answer 1

the poisson distribution is \[P(x,\lambda) = (e^{-\lambda}*\lambda ^{x})\div (x!)\]

Answer 2

i'm confused how to find X(bar) distribution and the probaility fr this distribution

Answer 3

if i use above formula, I get wrong answer