GATE DA 2026 Q54: Properties of the CDF of a discrete random variable

Let $X$ be a discrete valued random variable with cumulative distribution function $F(x)$ .

Which of the following statements is/are correct?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

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Answer: B, C (official GATE 2026 final answer key)

Concept used: Every CDF is non-decreasing and right-continuous, with limits 0 and 1; a discrete one is a step function.

First step: $F(x) = 0$ below the smallest value (so not always positive), and $F$ jumps at each value the variable takes.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key