The cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) is which of the following?
A) The area under f over all values x.
B) The area under f over all values that are x or less.
C) The area under f over all values that are x or more.
D) The area under f over all non-negative values that are x or less.

Question

Quizplus · Accepted Answer

The cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) is the area under f over all values that are x or less. This is because F(x) represents the probability that X takes on a value less than or equal to x, and this probability is the area under f up to x.

The Cumulative Distribution Function F(x) of a Continuous Random Variable