Zaymiey

📐 Mathematics  ·  Probability  ·  JEE

For a discrete random variable X: sum of all p(x) over all x must equal:

Answer: 1.

  • A 0
  • B μ
  • C 1
  • D n

Correct answer: C. 1

Explanation: Kolmogorov axioms: for any event A, P(A) ≥ 0; P(S) = 1. For a discrete RV, {X=x} are mutually exclusive events partitioning S, so Σₓ P(X=x) = P(S) = 1. This is the normalisation condition for any valid PMF.

UABA and BA onlyB onlyOutside both circles: complement of (A union B)

Venn diagram of the universal set U with events A and B, showing the intersection (A and B), the parts unique to each event, and the complement region outside both.

Concept context

Chance, events, conditional probability, and Bayes theorem

Read the full Probability notes →