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Suppose you throw a dart and it lands uniformly at random on a target which is a disk of unit radius. What is the probability density function $f(x)$ of the distance of the dart from the center of the disk?

  1. $f(x)=\left\{\begin{array}{ll}1, & \text { if } 0 \leq x \leq 1 \\ 0, & \text { otherwise }\end{array}\right.$
  2. $f(x)=\left\{\begin{array}{ll}2 x, & \text { if } 0 \leq x \leq 1 \\ 0, & \text { otherwise }\end{array}\right.$
  3. $f(x)=\left\{\begin{array}{ll}3 x^{2}, & \text { if } 0 \leq x \leq 1 \\ 0, & \text { otherwise }\end{array}\right.$
  4. $f(x)=\left\{\begin{array}{ll}4 x^{3}, & \text { if } 0 \leq x \leq 1 \\ 0, & \text { otherwise }\end{array}\right.$
  5. None of the above.
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