The unit interval (0, 1) is divided at a point chosen uniformly distributed over (0, 1) in R into two disjoint subintervals. The expected length of the subinterval that contains 0.4 is ___________. (rounded off to two decimal places)

GATE CSE 2025 Session 2 Q65: Expected length of the piece of (0,1) containing 0.4

The unit interval $(0, 1)$ is divided at a point chosen uniformly distributed over $(0, 1)$ in $\mathbb{R}$ into two disjoint subintervals.

The expected length of the subinterval that contains 0.4 is ___________. (rounded off to two decimal places)

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: 0.7 to 0.8 (official GATE 2025 final answer key)

Concept used: Expectation of a piecewise function of a uniform random variable.

First step: If the cut $U < 0.4$ , the piece containing 0.4 has length $1 - U$ ; otherwise it has length $U$ . Integrate each over its range.

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Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key