Which of the following condition should be satisfied by function for pmf?

The correct answer is A. The sum of all of the possible values is 1.

A probability mass function (pmf) is a function that assigns a probability to each possible value of a discrete random variable. The sum of the probabilities of all the possible values must be equal to 1. This is because the probability of any event must lie between 0 and 1, inclusive, and the sum of the probabilities of all possible events must be equal to 1.

Option B is incorrect because the sum of the probabilities of all the possible values must be equal to 1, not 0.

Option C is incorrect because the sum of the probabilities of all the possible values must be finite, not infinite.

Option D is incorrect because only option A is correct.