GATE 2025 CS (CS2) – Question 65
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)
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Show answer and explanation
Correct answer: 0.74
Explanation
If the cut point $U < 0.4$, the subinterval containing 0.4 has length $1-U$, and if $U > 0.4$ it has length $U$. $E = \int_0^{0.4}(1-u)\,du + \int_{0.4}^{1}u\,du = 0.32 + 0.42 = 0.74$.