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Previous Year Question (PYQs)
1
Let $X$ be a continuous random variable such that $E|X| < \infty$ and
$P\left(X \ge \frac12 + x\right) = P\left(X \le \frac12 - x\right)$ for all $x \in \mathbb{R}$.
Then:
Solution
The given condition shows symmetry about $\frac12$.
Hence both mean and median are $\frac12$.
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