X takes values in {1,2,3,4,5,6,7,8}. Pr(X=1)=Pr(X=2)=Pr(X=5)=Pr(X=7)=1/6 and Pr(X=3)=Pr(X=4)=Pr(X=6)

Q: What is GATE-CS?

GATE-CS is a competitive examination conducted in India. This question is from the 2026 GATE-CS Engineering Mathematics paper.

Q: How can I prepare for GATE-CS Engineering Mathematics?

To prepare for GATE-CS Engineering Mathematics, practice previous year questions (PYQs), understand concepts thoroughly, and solve mock tests regularly. This 2026 question covers Random Variables topic.

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This GATE-CS 2026 Engineering Mathematics question has a medium difficulty level and is marked as an important question.

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Question

X takes values in {1,2,3,4,5,6,7,8}. Pr(X=1)=Pr(X=2)=Pr(X=5)=Pr(X=7)=1/6 and Pr(X=3)=Pr(X=4)=Pr(X=6)=Pr(X=8)=1/12. The expected value E[X] = ___________.

Accepted Answer

Answer: 4.25Concept -- Expected Value of a Discrete Random Variable: E[X] = Σ x·P(X=x). Compute: 1·(1/6) + 2·(1/6) + 3·(1/12) + 4·(1/12) + 5·(1/6) + 6·(1/12) + 7·(1/6) + 8·(1/12). Sum the probabilities: four values have probability 1/6, four have 1/12, total = 4/6 + 4/12 = 8/12 + 4/12 = 1. Good. Sum = (1+2+5+7)/6 + (3+4+6+8)/12 = (15)/6 + (21)/12 = 2.5 + 1.75 = 4.25. Alternatively, 15/6 = 30/12, plus 21/12 = 51/12 = 4.25. Thus E[X] = 4.25. This calculation demonstrates the weighted average of outcomes with given probabilities.

X takes values in {1,2,3,4,5,6,7,8}. Pr(X=1)=Pr(X=2)=Pr(X=5)=Pr(X=7)=1/6 and Pr(X=3)=Pr(X=4)=Pr(X=6)=Pr(X=8)=1/12. The expected value E[X] = ___________.

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X takes values in {1,2,3,4,5,6,7,8}. Pr(X=1)=Pr(X=2)=Pr(X=5)=Pr(X=7)=1/6 and Pr(X=3)=Pr(X=4)=Pr(X=6)=Pr(X=8)=1/12. The expected value E[X] = ___________.

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