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Given a set $P$ of $n$ points in the plane, we study the computation of theprobability distribution function of both the area and perimeter of the convexhull of a random subset $S$ of $P$. The random subset $S$ is formed by drawingeach point $p$ of $P$ independently with a given rational probability $\pi_p$.For both measures of the convex hull, we show that it is \#P-hard to computethe probability that the measure is at least a given bound $w$. For$\varepsilon\in(0,1)$, we provide an algorithm that runs in$O(n^{6}/\varepsilon)$ time and returns a value that is between the probabilitythat the area is at least $w$, and the probability that the area is at least$(1-\varepsilon)w$. For the perimeter, we show a similar algorithm running in$O(n^{6}/\varepsilon)$ time. Finally, given $\varepsilon,\delta\in(0,1)$ andfor any measure, we show an $O(n\log n+ (n/\varepsilon^2)\log(1/\delta))$-timeMonte Carlo algorithm that returns a value that, with probability of success atleast $1-\delta$, differs at most $\varepsilon$ from the probability that themeasure is at least $w$.

Area and Perimeter of the Convex Hull of Stochastic Points