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Let us roll a six-sided dice n times. We suppose that the tosses are independent and random. Let $X_i$ be a random variable that takes $0$ if the number obtained belongs to {1, 2} or $1$ if the result belongs to {3, 4}, or $2$ if the number belongs to {5, 6}.

The questions is which probability distribution is this for $X_i$ / $1 \leq i \leq n$ ?

I am thinking this is not Binomial, Geometric, or Poisson, because there is no success/failure. I am just confused.

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  • $\begingroup$ If the die was fair, $X_i$ would be a discrete uniform. $\endgroup$
    – Glen_b
    Feb 22, 2022 at 13:11

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This is simply a discrete probability distribution with three possible outcomes, all of them equally probable.

The binomial, geometric and Poisson distributions are specific discrete distributions, but the term refers to any distribution with finitely or countably many possible outcomes.

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