# Normalization of Probability distribution [closed]

I need to Know. Is it a condition that Probability density is bounded between 0 and 1?

• I plotted a probability density versus the position and I got the maximum of the probability to be 1.25 – Ahmed M. Farouk Jun 4 '18 at 14:14
• This is a question about mathematics (probability) not physics. – sammy gerbil Jun 4 '18 at 14:18
• @sammygerbil Hmm... Is a question about quantum probabilities a mathematical question or a physics question? I think this is an important realization for people who are learning to do QM calculations. +1 – Bill N Jun 4 '18 at 14:43
• @BillN Is the question "What is 1+1=?" a question about physics just because addition is used in every branch of physics? The context of QM is not relevant to this question, and for that reason I think it is mathematics not physics. – sammy gerbil Jun 4 '18 at 15:02
• @sammygerbil Just because a question is off-topic here doesn't mean it is on-topic somewhere else. Please don't vote to migrate bad/unclear questions. Rather, just vote to close, but leave it here. Cheers! – AccidentalFourierTransform Jun 4 '18 at 15:50

It is not. For example, a uniform distribution in the interval $[0,1/2]$ has a probability density of $2$ everywhere in that interval.

Along the same lines, a uniform distribution in the interval $[0,1/n]$ has a probability density of $n$ everywhere in that interval, for any positive $n$. So probability density has no upper bound at all.