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The value of the distribution for any value of the random variable must be in the range [0, 1]. The sum (or integral) of the probability distribution function over all possible values of the random variable must be 1.
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1. It is a probability distribution function and so the area under the curve must be 1.
The mean must be 0 and the variance must be 1.
A probability distribution must have a well defined domain - that is, the set of possible outcomes.For each possible outcome, there must be a non-negative value associated - the probability of that outcome.The sum of the probabilities, over all possible outcomes, must be 1.