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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?

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Do you mean that each $X_i$,$i=1,\ldots,n$ follows a Poisson distribution? –  Eckhard Dec 19 '12 at 18:11
Yes, each one has Poisson distribution –  Johnny Dec 19 '12 at 18:23
What do you mean by $X_{1:n}$? In general, it is a good idea to define any notation that is not standard. –  Eckhard Dec 19 '12 at 19:44

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