Question

Which of the following is not the property of a distribution function \( F(x) \) of a random variable \( X \)?

• A. \( P(a \leq X \leq b) = F(b) - F(a) \)
• B. F(x) ≤ F(y) if x<y
• C. \( \lim_{x \to -\infty} F(x) = 0 \text{ and } \lim_{x \to \infty} F(x) = 1 \)
• D. \( F(1) = \frac{1}{2} \)

Hint:

When a question asks you to identify something that is “NOT a property,” look for options that specify an exact numerical value at a specific point (like \( F(1) = \frac{1}{2} \)). General properties must hold true for all possible distribution shapes, not just specific ones.

Answer 1

The Correct Option is D