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GATE 2025 ST – Question 39

Probability · Random Variables and Transforms · 2 marks · Multiple choice

X has CDF 0 for x<0, α(1+2x²) for 0≤x<1 and 1 for x≥1. Its median is 1/√2. Find α.

  1. 1/2
  2. 1/3
  3. 1/4
  4. 1/6

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Show answer and explanation

Correct answer: (C) 1/4

Explanation

The CDF is continuous at the stated interior median, so F(1/√2)=1/2. Substitution gives α(1+2·1/2)=2α=1/2. Thus **α=1/4, C**; the resulting boundary jumps are valid.

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