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This is a relatively straightforward question which I can't seem to find much help with. I ran across a question:

Identify the support of the following variable: Y + 1, where Y is a Bernoulli distribution

From my understanding of supports, it is the range of the outcomes where the probability is greater than 0. I know that Bernoulli trials only have two outcomes, however I don't know how to apply that information to the question. Any help is appreciated.

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You're mostly there: you've correctly defined the word support, but I suspect you're not clear on what the support is for a Bernoulli random variable.

You're right that Bernoulli trials have two outcomes. The Bernoulli random variable represents these outcomes, but by definition of being a random variable, the outcomes have to map to real numbers. The Bernoulli random variable is thus defined to take values 0 or 1 depending on the outcome from the trial.

Since $Y$ is Bernoulli, it has support $\{0,1\}$, so $Y+1$ must have support $\{1,2\}$

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  • $\begingroup$ Just so I can make sure I understand it, another problem said Y^2 where Y is binomial. Since Y has a support of {0,1}, Y^2 has a support of {0,1} too because 0^2 and 1^2 are the same results $\endgroup$ Sep 15, 2017 at 14:27
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    $\begingroup$ Binomial is not Bernoulli (usually)! They have different supports. If you want to find the support of a distribution you're not sure about, see Wikipedia, it actually has a summary table on the right for each distribution with its support. For example: en.wikipedia.org/wiki/Binomial_distribution has support $\{0,1,\dots,n\}$ $\endgroup$
    – RoryT
    Sep 15, 2017 at 14:35
  • $\begingroup$ I see, I made the erroneous assumption that binomial and bernoulli were the same! Thank you! $\endgroup$ Sep 15, 2017 at 14:59

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