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In: Statistics and Probability

X is a random variable following Poisson distribution. X1 is an observation (random sample point) of...

X is a random variable following Poisson distribution. X1 is an observation (random sample point) of X.

(1.1) Please find probability distribution of X and X1. Make sure to define related parameter properly.

(1.2) Please give the probability distribution of a random sample with sample size of n that consists of X1, X2, ..., Xn as its observations.

(1.3) Please give an approximate distribution of the sample mean in question 1.2(say, called Y) when sample size is 100 with detailed explanation.

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