For a **probability mass function (p.m.f.)** $f(x_i) = P[X = x_i]$, the two essential conditions are:
A$f(x_i) \geq 1$ for all $i$
B$f(x_i) \geq 0$ for all $i$, and $\sum_{i=1}^n f(x_i) = 1$
C$f(x_i) > 0$ for all $i$, and $\sum f(x_i) = 0$
D$\int f(x)\,dx = 1$
Answer & Solution
Correct answer: B. $f(x_i) \geq 0$ for all $i$, and $\sum_{i=1}^n f(x_i) = 1$
p.m.f. conditions: (i) each $p_i = f(x_i) \geq 0$; (ii) total probability over all possible values = 1. Together these ensure $f$ is a valid discrete probability distribution.
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