The cumulative distribution function is denoted and defined as which of the following?
A) f(x) and f(x) = P(X ≤ x)
B) f(x) and f(x) = P(X ≥ x)
C) F(x) and F(x) = P(X ≤ x)
D) F(x) and F(x) = P(X ≥ x)

Question

Quizplus · Accepted Answer

The cumulative distribution function is denoted as F(x) and defined as the probability that a random variable X is less than or equal to a certain value x (i.e. P(X ≤ x)). Therefore, option C is the correct choice. Option A is incorrect because f(x) usually represents the probability density function, not the cumulative distribution function. Option B is incorrect because it would be defined as P(X ≥ x) rather than P(X ≤ x). Option D is also incorrect for the same reason.

The Cumulative Distribution Function Is Denoted and Defined as Which