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Perhaps a silly question, but:

Let's say I want to randomly pick a number between 1-5, so that each number is equally likely to be picked. In other words, the number I pick is discrete Unif{1,5}.

Would this be equivalent to saying the distribution of picking each number is Bernoulli(0.2)?

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    $\begingroup$ Yes, marginally, but no jointly, that is the five indicators are not independent... $\endgroup$ – Xi'an Jan 27 '18 at 20:33
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Yes, marginally what you say is correct, but lack of independence means that this will not hold jointly.

If $X_i$ is the number of times the number $i$ is drawn, then jointly $(X_1, X_2, X_3, X_4, X_5)$ will have a multinomial distribution with parameters $(n=1, p_i=1/5, i=1,2,3,4,5)$.

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