Which statement about a CDF is true?

Which statement about a CDF is true?

• A. A CDF is always decreasing.
• B. A CDF is nondecreasing and approaches 1 as x increases.
• C. A CDF can take negative values.
• D. A CDF is defined only for discrete variables.

Answer: (B)

The main idea is that a CDF records the probability that the random variable is at most x, so when x grows, you’re including more possible outcomes. That makes the CDF nondecreasing: as you move to larger x, F(x) does not go down. As x grows larger and larger, you eventually include all possible outcomes, so F(x) approaches 1. The CDF always stays between 0 and 1, and it applies to any distribution, whether discrete, continuous, or mixed. It cannot be decreasing, cannot take negative values, and it isn’t limited to discrete variables.

The main idea is that a CDF records the probability that the random variable is at most x, so when x grows, you’re including more possible outcomes. That makes the CDF nondecreasing: as you move to larger x, F(x) does not go down. As x grows larger and larger, you eventually include all possible outcomes, so F(x) approaches 1. The CDF always stays between 0 and 1, and it applies to any distribution, whether discrete, continuous, or mixed. It cannot be decreasing, cannot take negative values, and it isn’t limited to discrete variables.