GATE DA 2025 Set 1 — Question 19
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Probability & Statistics → Continuous Random Variables → CDF (Continuous)
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Question
Let be a continuous random variable whose cumulative distribution function (CDF) , for some , is given as follows:If the median of is 3, then what is the value of ?
Correct answer
(A) 2
Solution
The median of a random variable is the value such that . Given that the median is 3, we have:Since is non-zero and non-one in the interval , and the median is 3, we assume . Using the given CDF formula for this interval:Checking the validity: If , the interval is . The value 3 lies within this interval. Thus, is the correct value.
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