The number of dirt specks on a randomly selected square yard of polyethylene film of a certain type has a Possion 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 be the resulting sample mean number of dirt specks. Obtain the first 21 probabilities in the X sampling distribution. [Hint: What does a moment generating function argument say about the distribution of X1+ …+ X;?]

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