Sampling Techniques in MATLAB

Planar geometry: expected area of random triangle, expected area/degree of convex hull. According to these instructions: A project will consist of a programming component (your sampling program) and a paper component (your report). There is no length requirement, but 10 pages should more than suffice for a typical report. The report should follow the following outline: Problem statement: what problem are you solving? E.g., in the case of card shuffling, the problem is to obtain a "perfect shuffle". So you need to state this, define perfect shuffle, and explain where the technical difficulties lie (in the case of shuffling, the state space has 52! elements). Note: to receive full credit here, you'll need a precise mathematical statement of the problem. Define your probability space, the distribution you want to sample from, etc. Methods: Give a precise mathematical description of the algorithm you are using to solve the problem in (1). Anybody who reads you paper should be able to reproduce your numerical results. Results: Present your simulation results in a visually comprehensible way (neat tables, charts, graphs, plots). Be sure to accompany each figure with a clear description of what it illustrates. Analysis: How "good" was your simulation – i.e., how close was it to the distribution you actually wanted to sample from? You'll need to define precisely your performance measure (measure of "goodness") and explain how you are computing it. In some cases, you should be able to provide a mathematical analysis of the results (e.g., "if I run my algorithm for 100 steps, then with probability at least .98 I'll be drawing from a distribution that is within .03 of the uniform distribution, under the total variation metric"). We'll discuss the requirements for each project on an individual basis.