Module 11: Cumulative Distribution Functions

Question 1

what is the def of CDF?

Answer 1

he cumulative distribution function (CDF) of a random variable X, de-noted by F (x), provides the probability associated with the event {X ≤ x}. In particular, for every x:

F(x) [ P({X <= x}) = SUM(p(k)) from k =< x if discrete and integral from negative infinity to x f(t), if continuous

Question 2

what are the CDF properties?

Answer 2

Non-decreasing

Right-continuous

Limits: lim⁡ 𝑥 → −∞ 𝐹(𝑥) = 0 lim x → −∞ F(x)=0,
lim⁡ 𝑥 → ∞ 𝐹(𝑥) = 1 lim x → ∞ F(x)=1

Bounded: 0 ≤ 𝐹(𝑥) ≤ 1