Question: can pmf be greater than 1?
Answer: No, a probability mass function cannot have a value above 1. Quite simply, all the values of the probability mass function must sum to 1. Also, they must be non-negative. ... The pdf if a non-continuous variable can never be more than 1, since (1) the sum of them must all add to 1 and (2) they must all be non-negative.