GATE CS 2026 Set 1 Q.58: Probability and Statistics

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

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

Your answer

Official answer and solution

Accepted answers: 4.24 to 4.26
From: Official GATE 2026 answer key

Solution

Compute $E[X] = \sum_{x=1}^8 x \Pr(X = x)$ .

By definition of expectation:

E[X] = \sum_{x=1}^8 x \Pr(X = x) = \frac{1 + 2 + 5 + 7}{6} + \frac{3 + 4 + 6 + 8}{12}

E[X] = \frac{15}{6} + \frac{21}{12} = 2.5 + 1.75 = 4.25

Final answer

4.25

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
Question: 58 of 65
Section: Computer Science and Information Technology

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