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TIFR ECE 2023 | Question-12

Consider a disk $D$ of radius $1$ centered at the origin. Let $X$ be a point uniformly distributed on $D$ and let the distance of $X$ from the origin be $R$. Let $A$ be the (random) area of the disk with radius $R$ centered at the origin. Then $\mathbb{E}[A]$ is

  1. $\frac{\pi}{3}$
  2. $\frac{\pi}{6}$
  3. $\frac{\pi}{4}$
  4. $\frac{\pi}{2}$
  5. None of the above

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