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.
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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 $1$).