Probability: limit of CDF

Dependencies: (incomplete)

1. Random variable

Let $X$ be a real random variable. Let $F_X$ be the CDF of $X$. Then \begin{align} \lim_{x \rightarrow -\infty} F_X(x) &= 0 & \lim_{x \rightarrow \infty} F_X(x) &= 1 \end{align}

Proof

See lemma 2.1.6 (a), page 28, [prob-and-rand-proc-book].

Dependency for: None

Info:

• Depth: 6
• Number of transitive dependencies: 12

Transitive dependencies:

1. /analysis/topological-space
2. /sets-and-relations/countable-set
3. /sets-and-relations/de-morgan-laws
4. σ-algebra
5. Generated σ-algebra
6. Borel algebra
7. Measurable function
8. Generators of the real Borel algebra (incomplete)
9. Measure
10. σ-algebra is closed under countable intersections
11. Probability
12. Random variable