An irregularly shaped object of unknown area A is located in the unit square 0 x 1, 0 y 1. Consider a random point distributed uniformly over the square; let Z = 1 if the point lies inside the object and Z = 0 otherwise. Show that E(Z) = A. How could A be estimated from a sequence of n independent points uniformly distributed on the square?

STAT 113: Statistics and Society Fall 2016, ONLINE Syllabus Lecturer: Ellen Gundlach Email: gundlach@purdue.edu (best way to contact) Office: HAAS 114 (phone: 765-496-6875) T.A.: Yixi Xu, xu573@purdue.edu Office hours: Most questions and problems can be handled through e-mail. If you send your TA a screenshot of the problem and talk us through your work, we can do pretty well that way. Allow 24 hours M-F for replies to your e-mails. Any student can visit the office hours of any instructor. We have many office hours available to you in the help room. See Blackboard Learn for a full list of