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