If I have a sample $X = (X_1,...,X_n)$ with Poisson distribution, and I have $Y = n\cdot X_{1:n}$ it has the same distribution with the same parameters or I have to change something?
distribution of Poisson random variables
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probability-distributions
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1What do you mean by $X_{1:n}$? In general, it is a good idea to define any notation that is not standard. – 2012-12-19