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I have a question in which it asks to verify whether if the uniform distribution is normalized. For one, what does it mean some distribution is normalized. For two, how do we go about verifying whether a distribution is normalized or not.

Dilip Sarwate
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Ada
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  • Thanks for the quick response. I understand that to normalize a random variable X is to (X-mean)/sd. This asks to verify uniform(a,b) is normalized. – Ada Sep 19 '13 at 23:26
  • Also asked on stats.SE where it has already received two answers. I have flagged it for closing. – Dilip Sarwate Sep 20 '13 at 03:14
  • Question was cross-posted to Cross Validated. – user642796 Sep 20 '13 at 07:05
  • @Ada: In the future, if you feel another Stack Exchange site is better suited for your question, please flag your question for moderator attention, expressing a desire to have it migrated to another specific Stack Exchange site. A moderator will then look into it, and if acceptable will migrate your question. Do not simply cross-post the question on multiple Stack Exchange sites. – user642796 Sep 20 '13 at 07:07
  • The answer provided by Christian Bueno is the correct one after confirming with the TA. I agree that there should only be one instance of this question, what should I do? – Ada Sep 21 '13 at 08:37

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A normalized distribution is one in which when you integrate over the entire domain, you get $1$. It's basically a requirement that states that the likelihood that something happens is $1$. For example the function $f(x)=1$ for $0\leq x \leq 2$ is not normalized (the integral is $2$) but $g(x)=1/2$ for $0\leq x \leq 2$ is normalized (the integral is $1$).

Christian Bueno
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