Let X be a random variable which takes values in the set \1, 2, 3, 4, 5, 6, 7, 8\. Further, (X = 1) = (X = 2) = (X = 5) = (X = 7) = 16 and (X = 3) = (X = 4) = (X = 6) = (X = 8) = 112. The expected value of X, denoted by E[X], is equal to ___________. (rounded off to two decimal places)

GATE CSE 2026 Session 1 Q58: Expected value of a discrete random variable on 1..8

Engineering Mathematics
2 marks
NAT
No negative marking

Let $X$ be a random variable which takes values in the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$ . Further, $\Pr(X = 1) = \Pr(X = 2) = \Pr(X = 5) = \Pr(X = 7) = \dfrac{1}{6}$ and $\Pr(X = 3) = \Pr(X = 4) = \Pr(X = 6) = \Pr(X = 8) = \dfrac{1}{12}$ .

The expected value of $X$ , denoted by $E[X]$ , is equal to ___________. (rounded off to two decimal places)

Try it: numerical answer: type the value

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Answer: 4.24 to 4.26 (official GATE 2026 final answer key)

Concept used: $E[X] = \sum x \Pr(X = x)$ .

First step: Group by probability: $\frac{1 + 2 + 5 + 7}{6} + \frac{3 + 4 + 6 + 8}{12}$ .

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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GATE CSE 2026 Session 1 Q58: Expected value of a discrete random variable on 1..8

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