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.
Related questions
Two coins tossed. P(both heads) =Bag has 4 red, 6 blue. P(red) =Probability of rolling 6 on a die:Probability of heads on a fair coin is:If a fair six-sided die is rolled twice, the probability that the sum is divisible by 3 isA bag has 3 red and 2 black balls. Probability of red ball drawn at random:Probability of getting an even number on rolling a single die:Probability of drawing a king from a standard deck of 52 cards: