GATE DA 2026 Set 1 — Question 54
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Probability & Statistics → Discrete Random Variables → CDF (Discrete)
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Question
Let be a discrete valued random variable with cumulative distribution function .Which of the following statements is/are correct?
Correct answer
(B) F(x) is a non-decreasing function.; (C) F(x) has jump discontinuity.
Solution
Option (A): A CDF takes values in . It can be 0 (e.g., for less than the minimum value in the support). Thus, it is non-negative, but not strictly positive everywhere. Incorrect.Option (B): By definition, a cumulative distribution function is non-decreasing. Correct.Option (C): For a discrete random variable, the CDF is a step function, which has jump discontinuities at the points where . Correct.Option (D): By definition, a CDF is right-continuous. For discrete variables, at a jump point , , so it is not left continuous. Incorrect.
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