MATH 632 Midterm: 2007 Math 632 - Seppalainen - Spring Exam 2
Document Summary
Instructions: show calculations and give concise justi cations for full credit. In-class part: consider a homogeneous rate poisson point process on the nonnegative real line. Let n (a) be the number of points in the subset a of [0, ). (a) (10 pts) given that there are 3 points in [0, t], what is the probability that there are. P {n [0, t] = 5 | n [0, 3t] = 7}. Now color each point blue with probability p and red with probability q = 1 p. colors of distinct points are independent. (c) (10 pts) let b3 be the location of the third blue point. Rules for take-home part: no consultation with anyone permitted. Not with fellow students, not with internet chat groups, nobody. Part is due by 12 noon tomorrow in the instructor"s o ce: crabs walk by the cave of the hungry octopus as a homogeneous rate poisson process.
