The GATE Grind

GATE 2022 ST – Question 29

Probability · Random Variables and Transforms · 1 mark · Numerical answer

X has density c(x−⌊x⌋) on 0<x<3,zero elsewhere. Find P(X∈[1/2,2]),to two decimals.

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Correct answer: 0.57 to 0.59

Explanation

Each of the three unit intervals contributes integral c/2,so c=2/3. Integrating the fractional part from .5 to 1 gives 3/8,and from 1 to 2 gives 1/2. Probability=(2/3)(7/8)=7/12≈**0.58**.

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