UNIVERSITY OF CALIFORNIA, SANTA CRUZ
BASKIN SCHOOL OF ENGINEERING
Department of Applied Mathematics
and Statistics
Student name:
Final exam: AMS263 - Spring 2008
1. Suppose that events occur according to a Poisson process with rate . Each time an
event oc
AMS-263 SPRING 2008
HOMEWORK 2 - DUE WEDNESDAY 04/22/08
(1) Assume that a student going to a certain four-year graduate school in norther California has,
each year, a probability q of unking out, a probability r of having to repeat and a probability
p of
AMS-263 SPRING 2008
HOMEWORK 2 - DUE THURSDAY 05/08/08
(1) Let cfw_Xn be random variables describing the population size after n periods of a branching
process such that X0 = 1 and the distribution of the size of of the offspring is p(x).
(a) Find an exp
#Contruct the transition matrix
P0 <- c(2/3,1/3)
P <- matrix(c(0.95,0.05,0.2,0.8),nrow=2,ncol=2,byrow=T)
E <matrix(c(1/6,1/6,1/6,1/6,1/6,1/6,0.1,0.1,0.1,0.1,0.1,0.5),nrow=2,ncol=6,byrow
=T)
#Generate a sequence of dice rolls
n <- 101
xt <- rep(0,n)
y <- r