GATE 2026 BM – Question 21

Engineering Mathematics · Probability and Statistics · 1 mark · Multiple choice

A coin gives heads with probability 1/3 and tails with probability 2/3. X=1 for heads and −1 for tails. Find Var(X).

Show answer and explanation

Correct answer: (C) 8/9

Explanation

The mean is 1×1/3−1×2/3=−1/3. Since X² is always one, E[X²]=1. Therefore Var(X)=E[X²]−E[X]²=1−1/9=8/9, C.

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