(1) That the probabilities lie between 0 and 1.
(2) The sum of all probabilities of the distribution sum up to 1.
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The mean must be 0 and the variance must be 1.
They are probability distributions!
Independent events with a constant probability of occurrence over a fixed interval of time (or space).
It is always non-negative. The sum (or integral) over all possible outcomes is 1.
A bell shaped probability distribution curve is NOT necessarily a normal distribution.